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DC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_44.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line Elm lieson G E A", "line Oak lieson F E D C", "line Plum lieson H D B" ], "circles": [], "semantics": [ "line Elm \\parallel line Plum", "m \\angle EDB = x", "m \\angle DEA = 55" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_57.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C A", "line C B", "line A B D" ], "circles": [], "semantics": [ "m \\angle ACB = 38", "m \\angle CBD = 10x+9", "m \\angle CAB = 7x+1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_70.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line D B C", "line A B", "line A C" ], "circles": [], "semantics": [ "AD \\perp DC on D", "AD = 8", "AC = 21.5", "DB = 15", "BC = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_82.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B C D E", "line A E", "line A C F" ], "circles": [ "\\odot D lieson B A E F" ], "semantics": [ "BC = y", "EA = 12", "FC = 5", "CE = x", "l \\widehat BA = l \\widehat BF" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_95.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "D" ], "lines": [ "line E D", "line B E", "line C D", "line B C" ], "circles": [], "semantics": [ "BC = 2", "BE = CD = 3", "ED = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_102.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "R", "T" ], "lines": [ "line S R", "line R T", "line S T" ], "circles": [], "semantics": [ "SR \\perp ST on S", "TS = 10\\sqrt{3}", "SR = 4\\sqrt{3}" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_104.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "B", "D", "N", "X" ], "lines": [ "line L N", "line B D", "line B X N", "line L B", "line L X D", "line N D" ], "circles": [], "semantics": [ "m \\angle BDX = m \\angle NLX" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_109.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B D", "line C D" ], "circles": [ "\\odot E lieson A B C" ], "semantics": [ "DB = 7.1", "AB = 2x", "CD = 9.8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_113.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "D", "B", "C", "F", "G", "H", "I", "J" ], "lines": [ "line G D H I", "line B C F H J", "line D F E", "line D C A", "line A E" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_122.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line C A" ], "circles": [], "semantics": [ "AB \\perp CA on A", "AC = 28", "AB = 20", "BC = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_124.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "N", "M", "O" ], "lines": [ "line L O", "line O N", "line N M", "line L M" ], "circles": [ "\\odot O lieson L N" ], "semantics": [ "m \\angle LON = 117", "m \\angle NML = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_131.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "M", "N", "O", "R" ], "lines": [ "line M R O", "line P R N", "line M N", "line M P", "line P O", "line N O" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_148.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "A", "R", "B", "Q", "P", "E", "F", "G", "H" ], "lines": [ "line F A P R Q B H", "line G C P D E" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_167.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "E", "H", "F", "J", "L", "A" ], "lines": [ "line G J H", "line L H", "line G A L", "line E J A F", "line J L" ], "circles": [ "\\odot A lieson G F H E" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_180.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "C", "D" ], "lines": [ "line F C", "line E D C", "line F E", "line F D" ], "circles": [], "semantics": [ "EC \\perp FD on D", "FC \\perp FE on F", "EF = 65", "FC = 72", "EC = 97" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_191.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "N", "M", "A" ], "lines": [ "line L A N", "line L M", "line M N" ], "circles": [ "\\odot A lieson L M N" ], "semantics": [ "LM = MN", "m \\angle MNA = 2x-5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_193.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "H", "D", "F", "C", "E", "G" ], "lines": [ "line A G C", "line B G", "line B A", "line B C", "line D H F", "line E F", "line E D", "line E H" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_194.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A D E", "line E C B" ], "circles": [ "\\odot F lieson A D C B" ], "semantics": [ "ED = x", "AD = 10", "EC = 3", "BC = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_196.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D C", "line D B A", "line A C", "line B C" ], "circles": [], "semantics": [ "AB = 8", "DB = 14", "CD = x", "AC = 20", "m \\angle DCB = m \\angle ACB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_197.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "F", "C", "B", "E", "H", "G", "I", "J" ], "lines": [ "line A I J C", "line A F B", "line C G B", "line D H C", "line D E A", "line E I F", "line F G", "line H J G", "line E H" ], "circles": [], "semantics": [ "EA = DE", "DH = HC", "GB = CG", "AF = FB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_202.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "B", "Q" ], "lines": [ "line A B", "line C B", "line D Q B" ], "circles": [ "\\odot Q lieson D C A B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_204.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "R", "S" ], "lines": [ "line Q P", "line Q R", "line P S R", "line Q S" ], "circles": [], "semantics": [ "QP = QS = PS = SR" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_207.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C A", "line C B" ], "circles": [], "semantics": [ "AB \\perp CB on B", "AB = 8", "AC = x", "CB = x-4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_214.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line E A", "line A B C", "line D B", "line E D C" ], "circles": [], "semantics": [ "EA \\parallel DB", "ED = 3x+11", "AB = 4y-7", "CD = ED = 5x-8", "CB = 2y-1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_225.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "M", "K", "L", "Q", "P" ], "lines": [ "line M P Q L", "line J Q K" ], "circles": [ "\\odot P lieson J M K L" ], "semantics": [ "ML \\perp JK on Q", "MP = 6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_226.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "T", "R", "S" ], "lines": [ "line S T", "line S R" ], "circles": [ "\\odot S lieson R T" ], "semantics": [ "TS = 8", "m \\angle RST = 72" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_243.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "G", "F", "D", "B" ], "lines": [ "line A B D", "line C B G", "line B F" ], "circles": [ "\\odot B lieson C D F G A" ], "semantics": [ "m \\angle DBC = 55", "m \\angle FBG = 35" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_247.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "D", "F" ], "lines": [ "line E F B", "line E D", "line B C D", "line A B", "line A F C" ], "circles": [], "semantics": [ "ED \\parallel AC", "m \\angle FBA = m \\angle FBC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_256.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line B D", "line A B", "line A C", "line C D" ], "circles": [], "semantics": [ "m \\angle CBA = 54", "m \\angle BCA = 36", "m \\angle BCD = 6x", "m \\angle CBD = 3y-3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_286.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "X", "Y" ], "lines": [ "line X Y", "line W Y", "line X W" ], "circles": [], "semantics": [ "XW = YW = 8", "m \\angle WYX = 4x-2", "m \\angle WXY = 62" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_287.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "D", "E", "A", "B", "C", "F" ], "lines": [ "line B D E", "line C A E" ], "circles": [ "\\odot F lieson D A P" ], "semantics": [ "m \\angle DEA = 84" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_314.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line \\ell lieson E F G B", "line m lieson J I H A", "line p lieson C G H L", "line n lieson D F I K" ], "circles": [], "semantics": [ "m \\angle GFD = m \\angle 1 = m \\angle HIF = m \\angle 2", "m \\angle JIF = m \\angle 3 = m \\angle BGH = m \\angle 4", "m \\angle IHG = m \\angle 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_334.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "J", "N", "M", "Q" ], "lines": [ "line N Q K", "line J N", "line N M", "line K M", "line J Q M", "line J K" ], "circles": [], "semantics": [ "JN \\perp JK on J", "NM \\perp KM on M" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_341.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "J", "L" ], "lines": [ "line K J", "line J L", "line K L" ], "circles": [], "semantics": [ "JL = 4x-8", "JK = KL = JL = x+7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_347.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "M" ], "lines": [ "line A M C", "line C D", "line B M D", "line B C", "line A B", "line A D" ], "circles": [], "semantics": [ "AD = BA = 15", "CD = BM = 6", "DM = 5", "m \\angle CMB = 92", "m \\angle MCD = 58" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_352.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "B", "F", "D", "C", "R" ], "lines": [ "line E F D", "line R F", "line C R", "line A C B" ], "circles": [ "\\odot R lieson A B D E" ], "semantics": [ "CR \\perp AB on C", "ED \\perp RF on F" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_353.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line A C", "line C B" ], "circles": [], "semantics": [ "AC \\perp CB on C", "AB = y", "AC = x", "CB = 3", "m \\angle CAB = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_367.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "N", "L", "M", "R", "P", "Q" ], "lines": [ "line R Q P", "line N Q M", "line L N K", "line L R M", "line K P M" ], "circles": [], "semantics": [ "NM \\perp LK on N", "LM \\perp KM on M" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_379.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "S", "T" ], "lines": [ "line R T", "line S T", "line R S" ], "circles": [], "semantics": [ "ST \\perp RS on S", "SR = 25", "RT = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_382.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line A C" ], "circles": [], "semantics": [ "CB \\perp AC on C", "AB = 65", "CA = x", "BC = 50" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_411.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "A", "E", "F" ], "lines": [ "line E C A F", "line B A", "line D C B", "line D A" ], "circles": [], "semantics": [ "EF \\perp DB on C", "DA = 2.5", "DC = CB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_416.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "G", "F", "H", "J", "L" ], "lines": [ "line E J L F", "line G J H" ], "circles": [ "\\odot L lieson G F H E" ], "semantics": [ "EF \\perp GH on J" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_417.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Y", "P", "W", "M", "A", "B", "C" ], "lines": [ "line Y W C", "line Y M B", "line A P Y", "line M W", "line P M" ], "circles": [], "semantics": [ "AY \\perp PM on P", "YC \\perp MW on W", "PM = MW", "m \\angle MYP = 4x-1", "m \\angle WYM = 2x+5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_433.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "Y", "Z", "X", "I", "U", "O" ], "lines": [ "line X U O", "line A Z O", "line Y Z I", "line X Z", "line E I", "line A E", "line E Z", "line I O", "line U Z", "line A Y", "line X Y" ], "circles": [], "semantics": [ "EA = AZ = ZO = 30", "EZ = YZ = ZI = XU = 25", "YX = 10", "ZX = 37", "ZU = IO = 18", "UO = 35" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_437.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line A B D", "line C D" ], "circles": [ "\\odot B lieson A D C" ], "semantics": [ "AC \\perp CD on C", "DC = AC = 12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_440.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "E", "B" ], "lines": [ "line D C", "line C B A", "line E B", "line D E A" ], "circles": [], "semantics": [ "DC \\parallel EB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_443.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line B C", "line D C", "line A D" ], "circles": [ "\\odot E lieson A B C D" ], "semantics": [ "m \\angle BAD = 85", "m \\angle BCD = 95", "m \\angle ABC = 105", "m \\angle CDA = 75" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_451.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line D B", "line C B", "line D C", "line D A" ], "circles": [], "semantics": [ "CB \\perp DC on C", "AB \\perp DB on B", "AB = x", "CD = z", "DA = 8", "BD = y", "m \\angle DAB = 60", "m \\angle CBD = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_456.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "V", "X", "M", "L", "N", "J", "Z", "Y", "K" ], "lines": [ "line V Z", "line Y Z", "line X Y", "line X W", "line W V", "line N J", "line M N", "line L M", "line L K", "line K J" ], "circles": [], "semantics": [ "MN \\perp LM on M", "LM \\perp LK on L", "VZ \\perp WV on V", "VZ \\perp YZ on Z", "LM = XW = XY = LK = MN = WV = YZ = KJ = NJ = VZ", "m \\angle XWV = m \\angle ZYX = m \\angle LKJ = m \\angle JNM", "m \\angle YXW = m \\angle NJK" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_457.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C B D", "line A D", "line A B", "line C A" ], "circles": [], "semantics": [ "CD \\perp AB on B", "CB = BD = y", "DA = CA = x", "BA = 8\\sqrt{3}", "m \\angle BDA = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_461.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "T", "R", "W", "V", "A" ], "lines": [ "line W A V", "line R V", "line T R", "line T A", "line T W" ], "circles": [], "semantics": [ "WV \\perp TA on A", "RT = 18", "WT = 12", "m \\angle TWA = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_468.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C D", "line E C B", "line A B", "line B D", "line E A", "line E D" ], "circles": [], "semantics": [ "AD = 17", "EB = 21" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_470.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Z", "W", "S", "X", "R", "Y" ], "lines": [ "line Z R S", "line W Y S", "line W X Z", "line X Y", "line Y R" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_471.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line B C D", "line A C E F", "line D E" ], "circles": [], "semantics": [ "m \\angle EDC = 22", "m \\angle BAC = 23", "m \\angle ABC = 32", "m \\angle BCE = m \\angle 1", "m \\angle DEF = m \\angle 3", "m \\angle CED = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_473.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C D", "line D E", "line A C E", "line A B" ], "circles": [], "semantics": [ "DE = 5", "AC = 2x", "EC = 9", "DC = x", "BC = 8", "m \\angle CAB = m \\angle DEC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_477.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "P", "B", "O", "C", "D" ], "lines": [ "line C A P", "line D B P", "line O B", "line A O" ], "circles": [ "\\odot O lieson A B" ], "semantics": [ "m \\angle BOA = x", "m \\angle APB = 40" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_480.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line B A", "line A C", "line C G", "line E F G", "line B E", "line D F" ], "circles": [], "semantics": [ "DF = 10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_489.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C D", "line A B E", "line B C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_497.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D", "E" ], "lines": [ "line D A C E", "line A B", "line B C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_507.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line B A", "line B C", "line D C" ], "circles": [ "\\odot D lieson B C A" ], "semantics": [ "DC = 1.5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_511.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "E" ], "lines": [ "line B C A", "line B D", "line A E D" ], "circles": [ "\\odot C lieson B E A" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_519.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "E", "F", "G", "H", "I", "J" ], "lines": [ "line E A G C H", "line I B G D F" ], "circles": [ "\\odot J lieson B C D A" ], "semantics": [ "m \\angle DGA = m \\angle 1", "m \\widehat AD = 134", "m \\widehat CB = 86" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_524.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "U", "Y", "X", "V", "Z", "W" ], "lines": [ "line Y X", "line X Z", "line Y Z", "line V W", "line U V", "line U W" ], "circles": [], "semantics": [ "UV = YX", "VW = YZ", "m \\angle XZY = m \\angle VWU" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_530.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "R", "Y", "X", "Z" ], "lines": [ "line Q R", "line P R", "line Q P", "line Z X", "line X Y", "line Z Y" ], "circles": [], "semantics": [ "PQ = 9", "QR = 12", "XY = 6", "YZ = 8", "m \\angle ZXY = m \\angle RPQ", "m \\angle RQP = m \\angle XYZ", "m \\angle QRP = m \\angle XZY" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_537.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "R", "S", "A", "B", "C" ], "lines": [ "line Q S B", "line Q P C", "line Q R A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_541.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "N", "R", "Q", "P" ], "lines": [ "line Q R N", "line M R P", "line Q P", "line M N", "line M Q", "line N P" ], "circles": [ "\\odot R lieson M N P Q" ], "semantics": [ "m \\angle RMN = m \\angle 1", "m \\angle RNM = m \\angle 8", "m \\angle RMQ = m \\angle 2", "m \\angle RNP = m \\angle 7", "m \\angle RQM = m \\angle 3", "m \\angle RPN = m \\angle 6", "m \\angle RQP = m \\angle 4", "m \\angle RPQ = m \\angle 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_545.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M" ], "lines": [ "line K I J D F", "line A B C D E", "line n lieson M J C G", "line m lieson L I B H" ], "circles": [], "semantics": [ "m \\angle KIB = 6x-144", "m \\angle MJD = 2x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_546.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line B D", "line A B", "line A C" ], "circles": [], "semantics": [ "AB \\perp AC on A", "BD \\perp AB on B", "CD \\perp AC on C", "CD \\perp BD on D", "DB = AC = 9", "CD = AB = 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_548.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line D F", "line G H", "line A B", "line E G", "line C A", "line C E", "line B D", "line H F" ], "circles": [], "semantics": [ "GH = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_558.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C" ], "lines": [ "line B A", "line A C", "line B C" ], "circles": [], "semantics": [ "AC = x-3", "BA = 2x-7", "BC = 4x-21" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_569.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line C A", "line C B", "line E D", "line E F", "line D F" ], "circles": [], "semantics": [ "AB \\perp CB on B", "ED \\perp DF on D", "AB = DF", "CA = EF", "m \\angle BAC = m \\angle 1", "m \\angle EFD = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_590.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "M", "H", "Q", "J" ], "lines": [ "line M H", "line H J P", "line M J Q", "line P Q" ], "circles": [], "semantics": [ "HJ = 9", "QP = 8.1", "QJ = 2y-1", "m \\angle JHM = 13y", "m \\angle JMH = 14y-8", "m \\angle PJQ = 53" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_601.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line B C", "line A C" ], "circles": [], "semantics": [ "BC \\perp AC on C", "AC = 9", "BC = 12", "BA = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_621.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "R", "Q", "A", "B", "C" ], "lines": [ "line Q C R", "line Q P", "line \\ell lieson A P C R B" ], "circles": [ "\\odot Q lieson C P" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_655.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B C", "line D C", "line D B", "line A D" ], "circles": [], "semantics": [ "DC \\perp AD on D", "AC \\perp DB on B", "AD = 8", "CD = 6", "CB = x", "AB = y", "AC = 10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_666.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line C A" ], "circles": [], "semantics": [ "CA = 23", "BC = x", "m \\angle BAC = 128", "m \\angle CBA = 21" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_675.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line C A" ], "circles": [], "semantics": [ "AB \\perp CB on B", "AB = BC = 3\\frac{1}{2}" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_691.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line A C", "line A D", "line B C D" ], "circles": [], "semantics": [ "AB = 24", "BC = x", "DC = 7", "AD = 20", "m \\angle BAC = m \\angle CAD" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_706.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B D", "line C D", "line A C", "line A B", "line A D" ], "circles": [], "semantics": [ "BD \\perp AB on B", "AC = CD = AB = BD = x", "AD = 17", "m \\angle DAB = y" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_722.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line G H", "line E C", "line A C", "line B D", "line A B", "line D F", "line F H", "line E G" ], "circles": [], "semantics": [ "AC = 4", "GH = 12", "EC = 5", "DF = 3", "FH = 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_732.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line B C" ], "circles": [], "semantics": [ "m \\angle ABC = 147" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_743.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "N", "M", "K", "L", "A", "B", "C", "D" ], "lines": [ "line D J N", "line C K N", "line N L B", "line N M A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_747.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line F D", "line D E", "line C E", "line A C", "line B A", "line B F" ], "circles": [], "semantics": [ "AB = CA = BF = EC = 25", "FD = DE = 28", "m \\angle ABF = m \\angle ECA = m \\angle CAB", "m \\angle DFB = m \\angle DEC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_754.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line C A", "line B C" ], "circles": [], "semantics": [ "BA \\perp BC on B", "CB = 9", "BA = 2\\sqrt{70}", "AC = 19", "m \\angle BAC = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_757.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line A B D", "line C D", "line C B" ], "circles": [], "semantics": [ "AB = 6", "CA = 12", "DC = 20", "DB = x", "m \\angle ACB = m \\angle DCB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_760.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "K", "L", "M" ], "lines": [ "line M L", "line J M", "line J K", "line K L" ], "circles": [], "semantics": [ "JK = 3f-6", "ML = 2f+8", "m \\angle JML = 3d-2", "m \\angle MJK = 56" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_762.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D" ], "lines": [ "line B C", "line C D", "line A D", "line B A" ], "circles": [], "semantics": [ "BA = CD", "m \\angle BCD = 3x+15", "m \\angle CBA = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_769.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B E D", "line A E C", "line D C", "line B C", "line A B", "line A D" ], "circles": [], "semantics": [ "AE = 6", "EC = 9", "BD = 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_775.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line q lieson H B C", "line F E B A", "line p lieson G E D" ], "circles": [], "semantics": [ "m \\angle FEG = m \\angle CBA" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_811.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "J", "K", "M", "A", "B" ], "lines": [ "line a lieson A B", "line J L", "line L M", "line J K", "line K M" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_821.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B", "E", "F" ], "lines": [ "line A C", "line A E D", "line D B", "line C E B" ], "circles": [ "\\odot F lieson A B D C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_826.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line B C", "line C D", "line A D" ], "circles": [], "semantics": [ "m \\angle BAD = m \\angle CDA = x", "m \\angle ABC = m \\angle BCD = 2x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_827.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line H F C A", "line r lieson E F G", "line s lieson D C B" ], "circles": [], "semantics": [ "m \\angle FCB = 3x", "m \\angle CFE = 2x+20" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_845.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q" ], "lines": [ "line k lieson P M J I F", "line m lieson E H J N Q", "line K A J C L", "line G B J D O" ], "circles": [ "\\odot J lieson A H B I C N D M" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_846.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "E", "D", "F", "G", "H", "I", "J", "K" ], "lines": [ "line I A F D J", "line G B F E K", "line F C H" ], "circles": [], "semantics": [ "m \\angle BFC = 6x", "m \\angle DFC = 3x", "m \\angle AFE = 12y-10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_857.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "N", "Q" ], "lines": [ "line N P", "line P Q", "line N Q" ], "circles": [], "semantics": [ "PQ \\perp NQ on Q", "PQ = 4", "NP = 13.6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_863.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C A", "line D C", "line C E" ], "circles": [], "semantics": [ "m \\angle DCE = 2x", "m \\angle DCB = m \\angle ECA = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_872.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C D", "line E D", "line A D", "line A C E", "line A B", "line B E" ], "circles": [], "semantics": [ "AC = 2.4", "BD = 16.4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_879.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "F", "I", "H", "A", "B" ], "lines": [ "line F G", "line G B H", "line I H", "line F A I" ], "circles": [ "\\odot A lieson F I", "\\odot B lieson G H" ], "semantics": [ "FG = 212", "IF = 100" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_883.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line C B", "line C A" ], "circles": [], "semantics": [ "CB \\perp CA on C", "CA = x", "BC = 13", "m \\angle ABC = 52" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_890.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B C D", "line E C", "line F B", "line F A", "line F E", "line E D" ], "circles": [], "semantics": [ "AD \\perp FB on B", "AD \\perp EC on C", "FE = 19", "CE = 20", "AB = 2", "CD = 10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_907.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "H", "D", "F", "C", "G", "J" ], "lines": [ "line D G C", "line B F C", "line A E B", "line A H D", "line H J F", "line E J G" ], "circles": [], "semantics": [ "AB \\perp AD on A", "AB \\perp EG on E", "AD \\perp HF on H", "HF \\perp EG on J", "BC \\perp HF on F", "DC \\perp EG on G", "DC \\perp BC on C", "AE = CF = b", "AH = CG = h" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_947.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J" ], "lines": [ "line E B", "line E H", "line B H", "line B C", "line C I", "line I F", "line D F", "line A D", "line A C", "line C F", "line F G", "line J G", "line I J", "line H I" ], "circles": [], "semantics": [ "BE = GJ = 10", "IJ = FD = 4", "HB = 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_959.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C", "line C E", "line D E", "line B D", "line B A" ], "circles": [], "semantics": [ "m \\angle DBA = m \\angle CAB = m \\angle ACE = m \\angle CED = m \\angle EDB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_979.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "T", "R", "S", "A" ], "lines": [ "line T S", "line R S", "line Q R", "line Q T", "line T A R", "line Q A S" ], "circles": [], "semantics": [ "RA = 14x-34", "TA = 12x-8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_985.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "R", "U", "V", "S", "T" ], "lines": [ "line R S T U", "line V T", "line V S", "line W R", "line W U" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_999.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "Z", "E" ], "lines": [ "line B E D", "line A D", "line C D", "line C E A", "line Z A", "line B A", "line B Z", "line B C" ], "circles": [ "\\odot Z lieson B C D A" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1001.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "D0", "D1" ], "lines": [ "line H G F", "line A B F", "line A C H", "line D E F" ], "circles": [ "\\odot D0 lieson A F H", "\\odot D1 lieson C B E G" ], "semantics": [ "DF = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1004.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "G", "A", "B", "C", "H" ], 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[ "A", "B", "C" ], "lines": [ "line B C", "line A C", "line A B" ], "circles": [], "semantics": [ "BC \\perp AB on B", "BA = BC = 9\\sqrt{2}", "CA = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1108.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "F", "D", "C", "E" ], "lines": [ "line D F", "line E F", "line E D", "line A C", "line B C", "line B A" ], "circles": [], "semantics": [ "m \\angle FED = m \\angle CBA", "m \\angle CAB = m \\angle FDE" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1114.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line G H", "line F H", "line E F", "line B E", "line A B", "line A D", "line C D", "line C G" ], "circles": [], "semantics": [ "DA = 5", "CG = 32", "GH = 24", "CD = 10", "FE = 6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1123.png", "style": "printed", "split": "test", "category": "plane 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B C", "line A E", "line E D", "line C D" ], "circles": [ "\\odot B lieson A C" ], "semantics": [ "AE = ED = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1150.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C" ], "lines": [ "line A B", "line D B", "line C D", "line A C" ], "circles": [ "\\odot C lieson A D" ], "semantics": [ "BD = 12", "AB = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1170.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P" ], "lines": [ "line G H I J", "line C D E F", "line K L M N", "line B E I M P", "line A D H L O" ], "circles": [], "semantics": [ "CF \\parallel GJ \\parallel KN", "DH = 3x-4", "IE = \\frac{2}{3}y+3", "HL = \\frac{5}{4}x+3", "IM = EI = \\frac{1}{3}y+6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1181.png", "style": "printed", "split": "test", "category": "plane 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"PGDP/printed/image/PGDP10K_new_1203.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "R", "S", "Q", "N", "M" ], "lines": [ "line M N", "line L N", "line L M", "line S R", "line S Q", "line R Q" ], "circles": [], "semantics": [ "ML = 2x+11", "QR = 3x-9", "m \\angle SRQ = 2y-40", "m \\angle LMN = y+10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1205.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "F", "D", "C", "V", "Z", "B", "T" ], "lines": [ "line E F", "line F D", "line Z D", "line V Z", "line E V T D", "line V F", "line F T Z", "line C B", "line B A", "line C A" ], "circles": [], "semantics": [ "EF = CB", "CA = FD" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1208.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "T", "R", "M", "L", "S" ], "lines": [ "line N L", "line M L", "line M N", "line R S", "line R T", "line T S" ], "circles": [], "semantics": [ "m \\angle LNM = m \\angle SRT = 55", "m \\angle NLM = m \\angle RST = 65", "m \\angle RTS = 2x+30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1228.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "T", "S" ], "lines": [ "line R S", "line T S", "line R T" ], "circles": [], "semantics": [ "RS \\perp TS on S", "RT = 7\\sqrt{2}", "ST = 3\\sqrt{2}" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1243.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "P", "L", "Y", "M", "X", "Z", "Q" ], "lines": [ "line L M", "line K P L", "line K M", "line P M", "line Y Z", "line Y Q", "line Z Q X", "line Y X" ], "circles": [], "semantics": [ "KL \\perp PM on P", "YQ \\perp ZX on Q", "KM = 20", "XY = 15", "YQ = x", "MP = 16", "m \\angle PKM = m \\angle QXY", "m \\angle PLM = m \\angle QZY" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1261.png", "style": "printed", "split": "test", "category": "plane 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23" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1281.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line B C D E A" ], "circles": [ "\\odot D lieson B A", "\\odot F lieson B C", "\\odot G lieson C D", "\\odot H lieson D E", "\\odot I lieson E A" ], "semantics": [ "BA = 48" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1283.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "R", "Q", "C", "B", "P", "D" ], "lines": [ "line C P B", "line A R B", "line Q D B", "line C D R", "line A Q C", "line A D P" ], "circles": [], "semantics": [ "m \\angle QAD = m \\angle RAD", "m \\angle RBD = m \\angle PBD", "m \\angle DCQ = m \\angle PCD" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1301.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line D C", "line B D", "line B A" ], "circles": [], "semantics": [ "BA = 4.5", "AC = a-1.4", "DB = BA = b-2.3", "CD = AC = 2a-7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1305.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "Y", "V", "W", "Z", "A", "B", "C", "D" ], "lines": [ "line X Z", "line C V X", "line X Y A", "line Z W B" ], "circles": [ "\\odot D lieson V X Z" ], "semantics": [ "m \\angle ZXV = 40", "m major \\widehat XZ = 180" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1311.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "F", "E", "D", "C", "G", "H", "I" ], "lines": [ "line B F C E", "line D E", "line F I H D", "line A G I C", "line A B", "line G B", "line H E" ], "circles": [], "semantics": [ "AC \\perp GB on G", "FD \\perp HE on H", "BE \\perp AB on B", "BE \\perp DE on E", "FC = 2", "EC = 1", "BF = 4", "BG = 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1318.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "T", "S", "R", "A", "B" ], "lines": [ "line Q S T", "line A S R B", "line T R", "line Q R" ], "circles": [], "semantics": [ "QT \\perp AB on S", "QR = 2x+3", "TR = 4x-7", "QS = ST" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1335.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "Q", "M", "R", "L" ], "lines": [ "line M R", "line Q R", "line N M", "line N Q", "line M L Q", "line N L R" ], "circles": [], "semantics": [ "NQ = 3x+2", "MN = 2y+5", "MR = 4x-2", "QL = 12", "RQ = 3y", "ML = w" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1337.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "V", "J", "L", "R", "A", "B" ], "lines": [ "line L A R", "line J A V" ], "circles": [ "\\odot B lieson J L V R" ], "semantics": [ "m \\angle LAJ = m \\angle 1", "m \\widehat VL = 56", "m \\widehat JR = 146" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1342.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line B D", "line A B", "line A C" ], "circles": [], "semantics": [ "AB \\perp AC on A", "BD \\perp AB on B", "CD \\perp AC on C", "CD \\perp BD on D", "BA = AC = CD = DB = 22.5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1359.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "N", "Q", "P" ], "lines": [ "line M P", "line N P", "line N M", "line N Q", "line Q P" ], "circles": [], "semantics": [ "NM = QP", "NQ = MP", "m \\angle PNQ = m \\angle MPN", "m \\angle NQP = m \\angle PMN" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1362.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B D", "line A C", "line C E", "line D E", "line C B" ], "circles": [], "semantics": [ "AD \\perp CB on B", "CE = x+15", "CB = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1365.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D", "O" ], "lines": [ "line A O", "line O D", "line B O", "line O C" ], "circles": [ "\\odot O lieson A B C D" ], "semantics": [ "m \\angle AOB = m \\angle DOC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1366.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line C D G", "line H G E", "line B E F", "line D B A" ], "circles": [], "semantics": [ "m \\angle GDB = 65", "m \\angle EBD = 105", "m \\angle GEB = 81", "m \\angle EBA = 75", "m \\angle GEF = 99", "m \\angle DGE = 109", "m \\angle DGH = 71", "m \\angle CDB = 115" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1374.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line B E", "line D E", "line A D", "line A C E", "line D C B" ], "circles": [], "semantics": [ "AB \\perp AD on A", "AB \\perp BE on B", "DE \\perp AD on D", "BE \\perp DE on E", "BE = 10", "ED = 16", "AC = CB = CE = DC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1389.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line E D", "line F D", "line B A", "line B C" ], "circles": [], "semantics": [ "m \\angle ABC = m \\angle 4", "m \\angle EDF = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1392.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line B C", "line A C D" ], "circles": [], "semantics": [ "m \\angle ABC = 65", "m \\angle BCD = 2x+10", "m \\angle BAC = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1396.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "I0", "I1" ], "lines": [ "line E F I G H", "line C M", "line A B C", "line A K", "line K L M", "line B D", "line J L" ], "circles": [ "\\odot I0 lieson E D H J", "\\odot I1 lieson F G" ], "semantics": [ "CM \\perp KM on M", "BD = JL = 80", "EF = HG = 50", "FG = 100", "BC = AK = CM = LM" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1399.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line C A" ], "circles": [], "semantics": [ "AB \\perp CA on A", "CA = 8", "AB = x", "BC = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1414.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E" ], "lines": [ "line A B", "line B C", "line D C", "line A D", "line B E D", "line A E C" ], "circles": [], "semantics": [ "AB \\parallel DC", "AB = 8", "DC = x", "BE = y", "AE = 6", "DE = 10", "CE = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1430.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line m lieson L I F C", "line s lieson A D F H", "line \\ell lieson J G D B", "line r lieson E G I K" ], "circles": [], "semantics": [ "line s \\parallel line r", "m \\angle FDG = m \\angle 4", "m \\angle IFD = m \\angle 6", "m \\angle DGI = m \\angle 5", "m \\angle FIG = m \\angle 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1432.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A B C", "line D A", "line D B", "line D C", "line E F G", "line H E", "line H F", "line H G" ], "circles": [], "semantics": [ "EG = 15", "AC = 12", "DB = x", "FH = 10", "AB = BC", "EF = FG", "m \\angle DAB = m \\angle HGF", "m \\angle BCD = m \\angle FEH" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1451.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "C" ], "lines": [ "line D A", "line B A" ], "circles": [ "\\odot C lieson D B" ], "semantics": [ "AB = 3x^{2}+2x-7", "DA = 2x+5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1452.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "L", "K", "M", "Q", "R", "S" ], "lines": [ "line K Q R M", "line N M", "line Q S N", "line L K", "line L S R" ], "circles": [], "semantics": [ "KQ = RM", "LS = SN = QS = SR", "LK = NM = QR", "m \\angle RMN = m \\angle QKL", "m \\angle KLS = m \\angle MNS" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1454.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line A B", "line B D", "line D G", "line F E G", "line C F", "line C G", "line C D", "line C B", "line A C", "line C E" ], "circles": [], "semantics": [ "FG \\perp CE on E", "EC = 5.6", "GF = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1462.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "F", "G", "H", "F'", "G'", "C", "H'", "E'" ], "lines": [ "line F G", "line G H", "line E H", "line F E", "line F' G'", "line G' H'", "line E' H'", "line F' E'" ], "circles": [], "semantics": [ "HE = 8", "H'E' = 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1472.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "S", "R", "A" ], "lines": [ "line P Q", "line Q R", "line S R", "line P A S" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1482.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "W", "Y", "Z" ], "lines": [ "line X Y", "line X Z", "line Y Z", "line W Y", "line W X" ], "circles": [], "semantics": [ "WX = 12", "YW = 14", "ZY = 17", "XZ = 18", "YX = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1487.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D", "E", "F", "G", "H" ], "lines": [ "line B F A", "line D F G C", "line B E C", "line E G", "line G H", "line A H C" ], "circles": [], "semantics": [ "BC \\perp EG on E", "GH \\perp AC on H", "EG = GH", "m \\angle GCE = m \\angle GCH" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1504.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "H", "B", "C", "G", "E", "F" ], "lines": [ "line B C", "line D C", "line A D", "line A B", "line F G", "line H G", "line E H", "line E F" ], "circles": [], "semantics": [ "AB = HE = 5", "BC = 6", "DA = 10", "GH = 4", "FG = 3", "CD = 8", "EF = 2.5", "m \\angle DAB = m \\angle HEF", "m \\angle GFE = m \\angle CBA", "m \\angle FGH = m \\angle BCD", "m \\angle CDA = m \\angle GHE" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1506.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "R", "U", "T", "A" ], "lines": [ "line U A S", "line R A T", "line U T", "line S T", "line R S", "line R U" ], "circles": [], "semantics": [ "US \\perp RT on A", "RA = TA = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1511.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line a lieson G H B", "line b lieson F D C", "line q lieson A H D E" ], "circles": [], "semantics": [ "line a \\parallel line b", "m \\angle BHD = 120", "m \\angle CDH = m \\angle 2", "m \\angle CDE = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1517.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "B", "A", "E", "C", "I", "D", "H", "F", "J", "K", "L", "M", "N", "O" ], "lines": [ "line K C F D M", "line H F I L", "line H E G O", "line J A E B N" ], "circles": [], "semantics": [ "JN \\parallel KM", "m \\angle AEH = 40", "m \\angle HFC = 70" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1525.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A E C", "line D E B", "line A B", "line C B", "line D A", "line D C" ], "circles": [], "semantics": [ "AC \\perp DB on E", "DC = 33", "CE = 25", "DE = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1531.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "F", "J", "G", "H", "O" ], "lines": [ "line E O H", "line F O J", "line O G" ], "circles": [ "\\odot O lieson E J H G F" ], "semantics": [ "m \\angle FOG = m \\angle HOG", "m \\widehat JH = 70" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1539.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "T", "A" ], "lines": [ "line A T" ], "circles": [ "\\odot T lieson A" ], "semantics": [ "AT = 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1542.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "E", "B", "D" ], "lines": [ "line A D B", "line A E C", "line C B", "line E D" ], "circles": [], "semantics": [ "ED \\parallel CB", "m \\angle ECB = m \\angle 3", "m \\angle AED = m \\angle 2", "m \\angle ADE = m \\angle 1", "m \\angle DBC = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1548.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line p lieson F C B", "line q lieson G E D", "line A C E H" ], "circles": [], "semantics": [ "m \\angle FCA = 110", "m \\angle GEH = 4x+10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1574.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C D", "line A C E" ], "circles": [], "semantics": [ "m \\angle ACD = m \\angle 11", "m \\angle ECD = m \\angle 12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1584.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C D", "line B C E", "line A B", "line B D", "line A E", "line D E" ], "circles": [], "semantics": [ "AD = 21", "BE = 32" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1602.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "X", "Z", "Y" ], "lines": [ "line Z Y", "line X Y", "line W X", "line W Z" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1606.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "N", "M", "Q", "R" ], "lines": [ "line P R M", "line R Q", "line N R" ], "circles": [ "\\odot R lieson N P Q M" ], "semantics": [ "PM \\perp NR on R", "m \\angle QRP = 115" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1609.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "U", "T", "A", "B" ], "lines": [ "line A T U N B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1613.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "J", "L", "K" ], "lines": [ "line K L", "line J K", "line J M", "line M L" ], "circles": [], "semantics": [ "ML = KL", "JK = JM", "m \\angle KJM = 59", "m \\angle MLK = 67" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1616.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "H", "E", "N", "M", "A", "B", "C" ], "lines": [ "line H C N", "line M N", "line M H", "line M C", "line A B M", "line S B E" ], "circles": [ "\\odot M lieson S A E N H" ], "semantics": [ "AM \\perp SE on B", "HN \\perp MC on C", "BM = MC", "m \\angle MHC = 40" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1620.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C A", "line A B", "line C B" ], "circles": [], "semantics": [ "AB \\perp CB on B", "AB = x", "BC = 16", "CA = 19" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1625.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line A D E", "line B C E F G", "line B A", "line B H", "line H E" ], "circles": [ "\\odot I lieson C H F D" ], "semantics": [ "AE \\perp HE on E", "AE \\perp BA on A", "BA \\perp BH on B", "m \\angle CBA = 60", "m \\widehat CH = 5x", "m \\widehat HF = 105" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1627.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C" ], "lines": [ "line A B", "line B C", "line D C", "line A D" ], "circles": [], "semantics": [ "m \\angle CDA = 83", "m \\angle BCD = 97" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1631.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "C", "X" ], "lines": [ "line A X C", "line A B", "line C B", "line D C", "line D A", "line D X B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1645.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "E", "F" ], "lines": [ "line D A E", "line B A" ], "circles": [ "\\odot F lieson B C A" ], "semantics": [ "m \\angle EAB = x", "m \\widehat BA = 136" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1650.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line B D", "line C D", "line A C" ], "circles": [], "semantics": [ "CA = BD = 4", "AB = DC = 7", "m \\angle DCA = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1651.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line B E", "line C E", "line A C", "line A D", "line D C", "line C B" ], "circles": [], "semantics": [ "AB \\perp AD on A", "AC \\perp DC on C", "AB \\perp BE on B", "m \\angle ABC = 31", "m \\angle BEC = 69", "m \\angle CAD = 38", "m \\angle ECB = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1652.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C B A", "line A D E" ], "circles": [ "\\odot F lieson C B D E" ], "semantics": [ "m \\angle BAD = m \\angle 1", "m \\widehat BD = 46", "m \\widehat EC = 120" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1664.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "X", "Y", "U", "V", "Z", "A", "B", "C", "D", "E" ], "lines": [ "line E Y Z V B", "line C X Z U D", "line A W Z" ], "circles": [], "semantics": [ "CD \\perp AZ on Z" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1666.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "F", "A" ], "lines": [ "line D A F", "line E F", "line D E" ], "circles": [ "\\odot F lieson A E" ], "semantics": [ "DE = 4", "FE = 3", "DF = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1669.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "B", "C", "D" ], "lines": [ "line A O C", "line A B D", "line C D" ], "circles": [ "\\odot O lieson A B C" ], "semantics": [ "m \\angle OAB = x", "m \\angle BDC = 43" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1671.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C", "line D C", "line A D", "line A B", "line D E B", "line A E C" ], "circles": [], "semantics": [ "BE = DE = 12", "CE = AE = 10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1699.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "K", "L", "M" ], "lines": [ "line M L", "line J M", "line J K", "line K L" ], "circles": [], "semantics": [ "ML = 6", "m \\angle JKL = 109" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1704.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B C", "line B D", "line C D", "line A E", "line A F", "line E F" ], "circles": [], "semantics": [ "CB = DC = BD = 4", "AF = EF = EA = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1708.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line E C A", "line B C D" ], "circles": [ "\\odot F lieson E B A D" ], "semantics": [ "m \\angle ECD = m \\angle 1", "m \\widehat DA = 46", "m \\widehat EB = 38" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1710.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C A", "line C B D", "line A D", "line B A" ], "circles": [], "semantics": [ "CD \\perp BA on B" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1711.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B", "E" ], "lines": [ "line A B", "line B E C", "line C D", "line A E D" ], "circles": [], "semantics": [ "CD \\parallel AB", "BA = 2", "AE = x-1", "DE = x+5", "DC = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1716.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D" ], "lines": [ "line A C", "line B C", "line C D" ], "circles": [], "semantics": [ "AC \\perp CD on C" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1721.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line E A B G", "line A C", "line F C D H", "line B D" ], "circles": [], "semantics": [ "m \\angle EAC = m \\angle 1", "m \\angle ACF = m \\angle 3", "m \\angle BAC = m \\angle 2", "m \\angle ACD = m \\angle 4", "m \\angle ABD = m \\angle 5", "m \\angle CDB = m \\angle 6", "m \\angle GBD = m \\angle 7", "m \\angle HDB = m \\angle 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1723.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "S", "V", "T", "A", "B" ], "lines": [ "line V T", "line S B T", "line R S", "line R A V", "line A B" ], "circles": [], "semantics": [ "SR = 26", "AB = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1727.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "F", "W'", "A", "B", "C", "D", "E", "G", "H" ], "lines": [ "line A W W' F", "line D C B F", "line H G E F", "line E W'", "line E B", "line G W", "line G C" ], "circles": [], "semantics": [ "FW' = 10.5", "WW' = x", "WF = 14" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1742.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line A B C", "line A F G", "line A E D", "line B E", "line E F" ], "circles": [], "semantics": [ "EB = 6x+1", "EF = 7x-4", "m \\angle AFE = m \\angle ABE = 90", "m \\angle FAE = m \\angle BAE = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1743.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "M", "P", "O", "N" ], "lines": [ "line M N", "line N O", "line O P", "line N P", "line L N", "line L M" ], "circles": [], "semantics": [ "MN \\perp LM on M", "NO \\perp OP on O", "LN = NP", "LM = NO", "MN = OP", "m \\angle MNL = m \\angle OPN", "m \\angle NLM = m \\angle ONP" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1744.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "R", "S", "T", "P", "A", "B" ], "lines": [ "line Q P B", "line R P T", "line Q T S", "line R B S", "line R A Q", "line A P S" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1750.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "R", "Q", "T", "S" ], "lines": [ "line P S R", "line P T Q", "line R Q", "line S T" ], "circles": [], "semantics": [ "m \\angle TQR = m \\angle PST" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1759.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "A", "K", "B", "C" ], "lines": [ "line N K", "line A C K", "line A B N", "line B C" ], "circles": [], "semantics": [ "NB = 2", "AC = 12", "KC = 3", "AB = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1763.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line A C", "line B A", "line B C", "line D C", "line A D" ], "circles": [], "semantics": [ "m \\angle ABC = 100" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1767.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line B D", "line A B", "line A C" ], "circles": [], "semantics": [ "AB \\parallel CD", "AB = CD" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1777.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B C", "line A B" ], "circles": [], "semantics": [ "BC \\perp AB on B", "AC = 16", "CB = x", "m \\angle BAC = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1791.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line B C", "line A C" ], "circles": [], "semantics": [ "AB \\perp BC on B", "AC = y", "AB = x", "BC = 7\\sqrt{2}", "m \\angle BCA = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1802.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line D B A", "line C D H", "line B E F", "line E H G" ], "circles": [], "semantics": [ "m \\angle CDB = x-11", "m \\angle DHG = x+10", "m \\angle EBA = 2x-42", "m \\angle HEF = 31" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1803.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "D", "G", "F", "C", "B" ], "lines": [ "line D C F", "line H B F", "line H G D", "line G C", "line B C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1811.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A D E", "line B C E" ], "circles": [ "\\odot F lieson B C D A" ], "semantics": [ "EC = 4", "BC = 2", "ED = 3", "AD = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1826.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Z", "W", "Y", "X", "P" ], "lines": [ "line W X", "line Z W", "line W P Y", "line Z Y", "line Y X", "line Z P X" ], "circles": [], "semantics": [ "WX \\perp ZW on W" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1837.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "L", "T", "Z", "Y", "W", "Q", "R", "S" ], "lines": [ "line X Y Z W", "line L Q W", "line L T X", "line L S Y", "line L R Z", "line T S R Q" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1852.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line A B", "line B D", "line C D" ], "circles": [], "semantics": [ "DC = 20", "BD = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1859.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Z", "W", "X", "Y" ], "lines": [ "line W Z", "line W X", "line X Y", "line Z Y" ], "circles": [], "semantics": [ "WX \\parallel ZY", "WZ = XY", "m \\angle ZWX = m \\angle WXY", "m \\angle WZY = m \\angle XYZ" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1880.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B C", "line A B" ], "circles": [], "semantics": [ "BA = 3.0", "CB = 1.2", "AC = x", "m \\angle ABC = 123" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1886.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "E" ], "lines": [ "line A E C", "line B E D", "line A B", "line B C", "line A D", "line D C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1903.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B" ], "lines": [ "line A B", "line C B", "line A C" ], "circles": [], "semantics": [ "CB \\perp AC on C", "AB = 26", "BC = 10", "CA = 24" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1928.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "R", "P", "Q", "A" ], "lines": [ "line R A P", "line S A", "line A Q" ], "circles": [ "\\odot A lieson S P Q R" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1932.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line c lieson K J H G", "line a lieson L J B C", "line b lieson I H E D", "line d lieson A B E F" ], "circles": [], "semantics": [ "m \\angle DEF = 2x", "m \\angle EHG = x+21", "m \\angle HJL = 136", "m \\angle JBA = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1936.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line F E", "line F D", "line E D", "line A B", "line B C", "line A C" ], "circles": [], "semantics": [ "m \\angle ACB = m \\angle DFE = 3x+y", "m \\angle BAC = 5x-y", "m \\angle DEF = m \\angle CBA = 148", "m \\angle EDF = 18" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1948.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "E" ], "lines": [ "line B E D", "line B C", "line A E C", "line A B", "line A D", "line D C" ], "circles": [], "semantics": [ "BD \\perp AC on E", "m \\angle EBA = m \\angle EBC = m \\angle EDA = m \\angle EDC", "m \\angle EAD = m \\angle ECD = m \\angle EAB = m \\angle BCE" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1956.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D" ], "lines": [ "line A C", "line A D B", "line C B", "line C D" ], "circles": [], "semantics": [ "AB \\perp CD on D", "BC = 18", "AD = 9", "m \\angle CAD = 60", "m \\angle ACD = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1987.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C", "line A B", "line B D", "line C D E" ], "circles": [], "semantics": [ "m \\angle CAB = 78", "m \\angle ABD = m \\angle ACD = m \\angle BDE = 102" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_1995.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A C E", "line B C D" ], "circles": [ "\\odot F lieson B A D E" ], "semantics": [ "DC = x", "AC = x+9", "BC = 8", "EC = 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2029.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M" ], "lines": [ "line M L", "line K M", "line K L", "line b lieson I J", "line F G", "line F H", "line H G", "line a lieson D E", "line A C", "line C B", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2032.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E", "F", "G" ], "lines": [ "line A D E", "line A C F", "line A B G", "line B C", "line D C" ], "circles": [], "semantics": [ "AE \\perp DC on D", "AG \\perp BC on B" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2040.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B E", "line C D E", "line A C", "line B D" ], "circles": [], "semantics": [ "CA = 72", "BD = 6x", "CD = DE", "BE = AB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2043.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "R", "Q", "T", "A", "S" ], "lines": [ "line T S R", "line A Q R", "line P A T", "line Q T", "line P Q S" ], "circles": [], "semantics": [ "TS = AT", "m \\angle QAT = m \\angle TSQ" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2044.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "B", "C" ], "lines": [ "line A O", "line B C O", "line B A" ], "circles": [ "\\odot O lieson C A" ], "semantics": [ "AO \\perp BA on A", "BA = 10", "AO = OC = x", "CB = 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2066.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D", "G" ], "lines": [ "line A B", "line B C", "line D C", "line A D" ], "circles": [ "\\odot G lieson A B C D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2078.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D C", "line B C", "line A B", "line B D" ], "circles": [], "semantics": [ "BC \\perp AB on B", "AC \\perp BD on D", "CD = 7", "AD = 21" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2083.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line C A", "line A B", "line B D", "line D F", "line F I", "line L I", "line J K L", "line H J", "line E H", "line C E", "line G K" ], "circles": [], "semantics": [ "JL \\perp GK on K", "LJ = 8", "GK = 12.3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2091.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "R", "Q" ], "lines": [ "line P Q", "line R Q", "line P R" ], "circles": [], "semantics": [ "RQ \\perp PR on R", "RP = q", "PQ = 8", "QR = p", "m \\angle QPR = 75" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2115.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "A", "B", "C", "D", "E", "F" ], "lines": [ "line F E A", "line F D C", "line A B C", "line A P D", "line F P B", "line E P C" ], "circles": [], "semantics": [ "FA \\perp AC on A", "FE = EA", "AB = BC", "FD = DC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2117.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C A", "line A B", "line C B" ], "circles": [], "semantics": [ "AB \\perp CB on B", "CA = y", "CB = x", "AB = 14\\sqrt{3}", "m \\angle CAB = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2118.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B A", "line B C" ], "circles": [], "semantics": [ "AB = 12", "BC = x", "m \\angle CBA = 118", "m \\angle BAC = 39" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2128.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A D", "line A B C", "line C E", "line B E", "line B D", "line D E" ], "circles": [], "semantics": [ "CE = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2133.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "M", "R", "Q", "O", "P", "A", "B", "C", "D", "E" ], "lines": [ "line A N O P R E", "line M P Q D", "line M O B", "line C M N" ], "circles": [], "semantics": [ "m \\angle ONM = m \\angle 6", "m \\angle NOM = m \\angle 7", "m \\angle OMN = m \\angle 5", "m \\angle POM = m \\angle 8", "m \\angle PMO = m \\angle 4", "m \\angle OPM = m \\angle 1", "m \\angle RPM = m \\angle 2", "m \\angle RPQ = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2134.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "P", "V", "L", "S", "T" ], "lines": [ "line V S", "line P L", "line J P", "line T V", "line T S", "line J L" ], "circles": [], "semantics": [ "JP = TV", "PL = VS", "JL = TS", "m \\angle PJL = m \\angle VTS", "m \\angle LPJ = m \\angle SVT", "m \\angle PLJ = m \\angle VST" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2149.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line B D", "line A D", "line A B", "line D C", "line A C" ], "circles": [], "semantics": [ "DC = BD", "m \\angle DAC = m \\angle 2", "m \\angle DAB = m \\angle 3", "m \\angle DCA = m \\angle 6", "m \\angle ADC = m \\angle 5", "m \\angle BDA = m \\angle 4", "m \\angle DBA = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2166.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D A", "line D C", "line C B", "line A B" ], "circles": [], "semantics": [ "DA \\perp DC on D", "DC \\perp CB on C", "DA \\perp AB on A", "CB \\perp AB on B", "AB = DC = DA = CB = 9" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2178.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line D C B", "line A C E F" ], "circles": [ "\\odot G lieson D A B F" ], "semantics": [ "AC = x", "BC = DC = 6", "FC = 9" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2184.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "J", "N" ], "lines": [ "line M J", "line J N", "line M N" ], "circles": [], "semantics": [ "MJ = 2x-5", "JN = x-2", "MN = 3x-9" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2197.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "I", "F", "G", "H", "A" ], "lines": [ "line I H", "line G H", "line I A G", "line F I", "line F A H" ], "circles": [], "semantics": [ "IH \\perp GH on H", "IH \\perp FI on I", "FI = GH" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2201.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "E" ], "lines": [ "line C B", "line A B", "line A D", "line D C" ], "circles": [ "\\odot E lieson D A B C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2237.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D B", "line B C", "line B A" ], "circles": [ "\\odot B lieson D C A" ], "semantics": [ "m \\angle ABD = 165", "m \\angle DBC = 145", "m \\angle ABC = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2240.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D B", "line A B", "line A D", "line D C", "line B C" ], "circles": [ "\\odot D lieson A C B" ], "semantics": [ "AB = BC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2280.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "Q", "R", "M", "P", "A", "B", "C", "D" ], "lines": [ "line D N Q", "line C M Q", "line Q P B", "line Q R A" ], "circles": [], "semantics": [ "m \\angle NQM = m \\angle PQR" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2281.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line B D", "line A B", "line A C" ], "circles": [], "semantics": [ "AB \\perp AC on A", "BD \\perp AB on B", "CD \\perp AC on C", "CD \\perp BD on D", "BA = CD = \\ell", "AC = DB = w" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2285.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "E", "F" ], "lines": [ "line A B C D E", "line F E", "line F D", "line F C", "line F B", "line F A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2313.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A C E", "line D C", "line B C F" ], "circles": [], "semantics": [ "AE \\perp DC on C", "m \\angle ECF = y", "m \\angle DCB = 3x+6", "m \\angle ACB = 2x+4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2317.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "S", "P", "Q", "T", "R" ], "lines": [ "line P Q", "line P R", "line Q R", "line M T", "line M S", "line S T" ], "circles": [], "semantics": [ "MS \\perp ST on S", "PQ \\perp QR on Q", "ST = PQ", "MS = QR" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2367.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "F", "D", "E" ], "lines": [ "line F E D", "line C D", "line A B C", "line A F", "line B E" ], "circles": [], "semantics": [ "AC \\perp AF on A", "AC \\perp BE on B", "CD \\perp AC on C", "FD \\perp AF on F", "FD \\perp BE on E", "FD \\perp CD on D", "AB = 36", "DE = x", "DC = 12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2372.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "E" ], "lines": [ "line A E D", "line B D", "line B E", "line B A", "line B C", "line C D" ], "circles": [], "semantics": [ "AD \\perp BE on E", "AD = 5", "BE = 4", "BA = CD", "BC = ED" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2377.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "A", "B", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line J A C E", "line I B D F", "line K A B H", "line L C D G" ], "circles": [], "semantics": [ "KH \\parallel LG", "JE \\parallel IF", "m \\angle IBA = m \\angle 3", "m \\angle BAJ = m \\angle 1", "m \\angle LCA = m \\angle 2", "m \\angle CDB = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2379.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "J", "L", "A" ], "lines": [ "line K J", "line K L" ], "circles": [ "\\odot A lieson K L J" ], "semantics": [ "m \\widehat JL = 92" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2380.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B A", "line C A", "line C B", "line E D", "line D F", "line E F" ], "circles": [], "semantics": [ "BC = FE = 12", "BA = 20", "DE = y+4", "AC = 2x", "DF = 15", "m \\angle DEF = m \\angle BCA", "m \\angle ABC = m \\angle FDE", "m \\angle EFD = m \\angle BAC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2399.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line B C" ], "circles": [ "\\odot D lieson A B C" ], "semantics": [ "m \\angle ABC = x", "m major \\widehat AC = 230" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2413.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "E", "F" ], "lines": [ "line A E F B", "line A D", "line D E", "line C F", "line D C", "line C B" ], "circles": [], "semantics": [ "DC \\parallel AB", "AB \\perp DE on E", "AB \\perp CF on F", "DC = z", "EF = 6", "AD = 8", "DE = x", "AE = y", "m \\angle DAE = 30", "m \\angle CBF = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2426.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Y", "X", "Z" ], "lines": [ "line X Y", "line X Z", "line Y Z" ], "circles": [], "semantics": [ "YX = XZ = 4", "m \\angle XYZ = m \\angle XZY = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2432.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line A B", "line C B", "line D C", "line E D", "line F E", "line F G", "line G A" ], "circles": [], "semantics": [ "FE = ED = FG = DC = CB = GA = AB", "m \\angle CDE = m \\angle DEF = m \\angle EFG = m \\angle BAG = m \\angle ABC = m \\angle BCD = m \\angle FGA" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2434.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "V", "Q", "R", "T", "U", "S", "W", "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line C V W R D", "line A P W T G", "line B Q W U F", "line W S E" ], "circles": [], "semantics": [ "m \\angle PWQ = m \\angle 2", "m \\angle RWQ = m \\angle 3", "m \\angle RWS = m \\angle 4", "m \\angle VWU = m \\angle 7", "m \\angle TWS = m \\angle 5", "m \\angle TWU = m \\angle 6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2443.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line k lieson C D", "line A B" ], "circles": [ "\\odot E lieson A B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2453.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E" ], "lines": [ "line A E", "line B E", "line B A", "line E C", "line D C", "line E D" ], "circles": [], "semantics": [ "m \\angle CED = m \\angle ECD", "m \\angle EBA = m \\angle AEB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2482.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P" ], "lines": [ "line A C H L O", "line E C D F", "line B D I M P", "line G H I J", "line K L M N" ], "circles": [], "semantics": [ "CH = 20-5x", "DI = y", "HL = CH = 2x+6", "IM = DI = \\frac{3}{5}y+2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2490.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C" ], "lines": [ "line B C", "line A C", "line A B" ], "circles": [], "semantics": [ "AB = x", "BC = 9", "CA = 11", "m \\angle BCA = 28" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2494.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "N", "K", "L", "M", "Q" ], "lines": [ "line N Q K", "line J Q L", "line M Q" ], "circles": [ "\\odot Q lieson N J K L M" ], "semantics": [ "m \\angle NQM = 55", "m \\angle KQL = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2516.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A F", "line D E F", "line C D", "line C B A", "line B E" ], "circles": [], "semantics": [ "CD \\parallel AF", "DC = 4", "AF = x", "BE = 7", "CB = BA", "DE = EF" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2557.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "T", "H", "R", "A" ], "lines": [ "line M R T", "line T H", "line R H", "line M H" ], "circles": [ "\\odot A lieson T H M" ], "semantics": [ "MT \\perp RH on R" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2558.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D" ], "lines": [ "line A D", "line C D", "line B C", "line B A" ], "circles": [], "semantics": [ "BC \\perp BA on B", "CD \\perp BC on C", "AD \\perp BA on A", "AD \\perp CD on D", "CD = AD = BC = BA" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2566.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line D C", "line B C F", "line E F", "line D E", "line A D" ], "circles": [], "semantics": [ "AB \\perp AD on A", "AB \\perp BF on B", "DC \\perp AD on D", "DC \\perp BF on C", "BF \\perp EF on F", "AB = 20", "AD = DE = 10", "EF = 12", "BF = 18" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2575.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Y", "V", "Z", "U", "S", "T" ], "lines": [ "line Y T Z", "line V U Z", "line Y S V", "line S T", "line T U", "line S U" ], "circles": [], "semantics": [ "SV = YS", "YT = TZ", "UZ = VU" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2590.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C B", "line A C E", "line E D", "line B D", "line A B" ], "circles": [], "semantics": [ "CB \\perp AE on C", "BA = 20", "DB = 15", "m \\angle BAC = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2594.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "B" ], "lines": [ "line D C", "line B C", "line A B", "line A D" ], "circles": [], "semantics": [ "m \\angle CBA = 133", "m \\angle CDA = 80", "m \\angle BAD = 32x+15", "m \\angle DCB = 44x-1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2600.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "K", "H", "M", "G", "L", "F" ], "lines": [ "line H F L", "line J H G", "line K L M", "line K F" ], "circles": [ "\\odot F lieson J K M G" ], "semantics": [ "HL \\perp JG on H", "HL \\perp KM on L", "HF = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2604.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D E B", "line C E A", "line D C", "line D A", "line A B", "line C B" ], "circles": [], "semantics": [ "DC = 4", "CE = EA", "EB = DE", "m \\angle BCE = 58" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2606.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "F", "D", "E", "G" ], "lines": [ "line A D F G E B", "line C B", "line C E", "line C G", "line C F", "line C D", "line A C" ], "circles": [], "semantics": [ "m \\angle CFG = 77", "m \\angle CAD = 42", "m \\angle GCE = m \\angle 4", "m \\angle FCG = m \\angle 3", "m \\angle DCA = m \\angle 1", "m \\angle DCF = m \\angle 2", "m \\angle BCE = m \\angle 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2636.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line D B", "line B C", "line A C" ], "circles": [ "\\odot D lieson A B C" ], "semantics": [ "DB = 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2658.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line B D", "line C D", "line A C" ], "circles": [], "semantics": [ "AB \\perp AC on A", "DC = AB = 8", "BD = AC = 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2662.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "G", "H", "J", "A" ], "lines": [ "line G F", "line G A J", "line G H", "line F A H", "line J H", "line F J" ], "circles": [], "semantics": [ "GA = 12", "HA = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2670.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line B D", "line A B", "line A C", "line A D" ], "circles": [], "semantics": [ "BD \\perp AB on B", "CD \\perp AC on C", "BA = 40", "DB = 32", "DA = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2679.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "M", "O", "N", "A" ], "lines": [ "line M P", "line P N", "line N O" ], "circles": [ "\\odot A lieson M P O N" ], "semantics": [ "m \\angle ONP = 56", "m \\widehat NM = 70" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2683.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line B A", "line B C", "line C D" ], "circles": [], "semantics": [ "BA \\perp BC on B", "AD \\perp BA on A", "BC = 15", "AB = 6", "AD = 17" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2684.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "T", "S", "M", "B" ], "lines": [ "line C S T", "line C B A", "line B M", "line M S" ], "circles": [ "\\odot M lieson A T C" ], "semantics": [ "CA \\perp BM on B", "CT \\perp MS on S", "CA = 42", "BM = MS" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2698.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "D", "C" ], "lines": [ "line A C", "line E C", "line E D", "line C D", "line B A", "line B C" ], "circles": [], "semantics": [ "AC = CD", "BC = EC", "BA = ED", "m \\angle ABC = m \\angle CED", "m \\angle CAB = m \\angle EDC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2707.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "S", "X", "W", "Q", "R", "T", "V", "U" ], "lines": [ "line P Q", "line Q R", "line P R", "line S U", "line S T", "line U T", "line X W", "line V W", "line X V" ], "circles": [], "semantics": [ "VW = ST = PR", "m \\angle QPR = m \\angle SUT = m \\angle WVX", "m \\angle QRP = m \\angle XWV = m \\angle STU" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2724.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line D C", "line B D", "line B A" ], "circles": [], "semantics": [ "BA = BD = DC = AC", "m \\angle CDB = 130" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2729.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C B", "line B D", "line C D E", "line A E", "line D A" ], "circles": [], "semantics": [ "DA \\parallel CB", "CD = z", "ED = 45", "EA = 55", "BD = 44", "m \\angle BCD = m \\angle EDA", "m \\angle EAD = m \\angle CBD" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2733.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line A C", "line B C" ], "circles": [], "semantics": [ "AC \\perp BC on C", "CB = 18", "BA = 27" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2737.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "S", "R" ], "lines": [ "line Q R", "line P S", "line P Q", "line S R" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2740.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A B C D", "line F C E", "line F H", "line G F B" ], "circles": [], "semantics": [ "m \\angle HFG = m \\angle 9", "m \\angle CFH = m \\angle 8", "m \\angle CFB = m \\angle 7", "m \\angle ABF = m \\angle 1", "m \\angle CBF = m \\angle 2", "m \\angle BCF = m \\angle 3", "m \\angle DCF = m \\angle 4", "m \\angle BCE = m \\angle 5", "m \\angle DCE = m \\angle 6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2756.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line C D", "line B C", "line B A", "line A D", "line H E", "line H G", "line G F", "line E F" ], "circles": [], "semantics": [ "DC = x", "GF = 24" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2766.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D A", "line D C", "line A B C", "line D B" ], "circles": [], "semantics": [ "DC = y", "CB = 8", "AD = 30", "CA = 28", "m \\angle BDA = m \\angle BDC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2773.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line B C D", "line A D", "line A C" ], "circles": [], "semantics": [ "BD \\perp AC on C", "m \\angle BAC = m \\angle DAC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2779.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D" ], "lines": [ "line B A", "line B C", "line C D", "line A D" ], "circles": [], "semantics": [ "m \\angle ABC = m \\angle DCB = 2x", "m \\angle CDA = m \\angle BAD = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2786.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "D", "B", "C", "F" ], "lines": [ "line D F", "line D C", "line B F C", "line E B", "line A E D", "line A B" ], "circles": [], "semantics": [ "AE = FC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2789.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line B D", "line C D", "line A C" ], "circles": [], "semantics": [ "AB \\perp AC on A", "CD \\perp AC on C", "BD \\perp CD on D", "AB \\perp BD on B", "BD = AB = AC = CD = s" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2805.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D" ], "lines": [ "line C B", "line A D B", "line A C", "line C D" ], "circles": [], "semantics": [ "AB \\perp CD on D", "CB \\perp AC on C", "AD = x", "CD = z", "BD = y" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2851.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "F", "D", "E", "G", "H", "I", "J", "K", "L" ], "lines": [ "line G A B H", "line A C I", "line A D L", "line B E J", "line B F K" ], "circles": [], "semantics": [ "m \\angle HBF = 86", "m \\angle CAD = 33", "m \\angle EBF = 35", "m \\angle BAD = 87" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2863.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "W", "Y", "Z" ], "lines": [ "line W Z Y", "line X Y", "line X Z", "line W X" ], "circles": [], "semantics": [ "WY \\perp XZ on Z", "WZ = ZY", "WX = XY", "m \\angle YXZ = m \\angle ZXW", "m \\angle ZYX = m \\angle ZWX" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2891.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C", "line B C D", "line C E" ], "circles": [], "semantics": [ "AC \\perp BD on C", "m \\angle ECD = 2x", "m \\angle BCA = 3x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2895.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "D", "E" ], "lines": [ "line E D", "line E F" ], "circles": [ "\\odot E lieson D F" ], "semantics": [ "ED = 6", "m \\angle DEF = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2901.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "M", "N" ], "lines": [ "line M N", "line P N", "line M P" ], "circles": [], "semantics": [ "MN \\perp MP on M", "PM = 12", "NP = 37", "MN = 35" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2909.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B" ], "lines": [ "line A B", "line A C", "line C B" ], "circles": [], "semantics": [ "AC = 28", "CB = x", "m \\angle BAC = 35", "m \\angle ABC = 48" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2911.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line \\ell lieson A F G", "line B D", "line C E", "line D F", "line C B", "line E F" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2915.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "N", "L", "O" ], "lines": [ "line M N", "line L O N", "line L M" ], "circles": [ "\\odot L lieson O M" ], "semantics": [ "MN = 4", "LM = 3", "NO = 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2922.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Y", "W", "P", "Z", "X" ], "lines": [ "line W X Y", "line Y Z", "line W P Z", "line X P" ], "circles": [], "semantics": [ "XP \\parallel YZ" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2923.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "P", "Q", "Y" ], "lines": [ "line X Y", "line P Q" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2937.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "F", "D", "E" ], "lines": [ "line C F", "line C D", "line D E", "line F E", "line A F", "line B A", "line B C" ], "circles": [], "semantics": [ "BA = DE", "BC = CD", "AF = FE", "m \\angle FCB = m \\angle FCD = 60", "m \\angle CFA = m \\angle CFE = 50", "m \\angle ABC = m \\angle CDE = 120", "m \\angle FAB = m \\angle DEF = 130" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2963.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "R", "S" ], "lines": [ "line Q P", "line P S", "line R S", "line Q R" ], "circles": [], "semantics": [ "PS \\perp RS on S", "PS = 3", "SR = 6", "m \\angle PQR = 88" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2972.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B", "E" ], "lines": [ "line D C", "line A B C", "line A E D", "line E B" ], "circles": [], "semantics": [ "EB \\parallel DC", "AB = x+2", "CB = 6", "DE = 5", "AD = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2978.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line C A" ], "circles": [], "semantics": [ "AB \\perp CA on A", "CA = 22", "AB = 20", "BC = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2984.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "D", "C" ], "lines": [ "line A B", "line A C D", "line E D", "line B C E" ], "circles": [], "semantics": [ "AD \\perp ED on D", "AB \\perp AD on A", "CE = BC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2986.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B C", "line D C", "line F E D", "line F A", "line E B" ], "circles": [], "semantics": [ "FA \\parallel DC", "FA = 7", "CD = 3", "AB = BC", "FE = ED" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2987.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "G", "A", "D" ], "lines": [ "line R A D", "line G R", "line G D", "line G A" ], "circles": [ "\\odot D lieson G A" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2989.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "K", "L", "M" ], "lines": [ "line J M L", "line K L", "line K J", "line K M" ], "circles": [], "semantics": [ "JL \\perp KM on M" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_2995.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line C J I H", "line D K L G", "line B J K E", "line A I L F" ], "circles": [], "semantics": [ "BE \\parallel AF", "DG \\parallel CH", "m \\angle KJC = 5z+2", "m \\angle JKL = x", "m \\angle ILK = 68", "m \\angle ILG = 4y" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3012.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line A E", "line E D", "line C D", "line A C" ], "circles": [], "semantics": [ "AB = 9" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3025.png", "style": "printed", "split": 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"split": "test", "category": "plane geometry", "points": [ "X", "Y", "M", "A", "B" ], "lines": [ "line k lieson B M A", "line X M Y" ], "circles": [], "semantics": [ "line k \\perp XY on M", "XM = MY" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3220.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A B C", "line E D C", "line G F E", "line G H A", "line H B", "line H F", "line F D", "line B D" ], "circles": [], "semantics": [ "GE \\perp GA on G", "EC \\perp GE on E", "AC \\perp GA on A", "AC \\perp EC on C", "GH = EF = CD = AB = 3", "AH = GF = ED = CB = 6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3240.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "B", "D", "C" ], "lines": [ "line A B", "line B C", "line D C", "line E D", "line A E" ], "circles": [], "semantics": [ "AB \\perp AE on A", "AB \\perp BC on B", "DC \\perp ED on D", "m \\angle BCD = m \\angle DEA" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3263.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "C", "A", "F", "D" ], "lines": [ "line B C", "line A C", "line F E", "line F D", "line B A", "line E D" ], "circles": [], "semantics": [ "ED = x-3", "BA = 6", "FD = x+1", "AC = 12", "m \\angle FED = m \\angle CBA = 40", "m \\angle CAB = m \\angle FDE", "m \\angle EFD = m \\angle BCA" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3272.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line m lieson A C E", "line n lieson B C D" ], "circles": [], "semantics": [ "line m \\perp line n on C" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3276.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "X", "Z", "Y" ], "lines": [ "line W Y Z", "line X Z", "line X W", "line X Y" ], "circles": [], "semantics": [ "XY = XW = YZ", "m \\angle XYZ = 128" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3282.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A D F", "line A B", "line E D B" ], "circles": [ "\\odot C lieson A B F E" ], "semantics": [ "m \\angle DAB = a", "m \\angle ABD = b", "m \\angle FDE = c", "m \\widehat BF = 108", "m \\widehat EA = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3293.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O" ], "lines": [ "line K I J B O L", "line A C D L", "line A N E K", "line H F", "line G B" ], "circles": [ "\\odot F lieson E C M I H", "\\odot G lieson M D B J" ], "semantics": [ "HF = 5", "GB = AN = 3", "OL = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3296.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ 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"C", "D", "E", "F", "G", "H" ], "lines": [ "line A B C", "line C E H", "line A D F", "line F G H" ], "circles": [ "\\odot P lieson D B E G" ], "semantics": [ "AC \\perp AF on A", "AC \\perp CH on C", "AF \\perp FH on F", "CH \\perp FH on H", "AC = 9" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3332.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line A C", "line D C", "line B C" ], "circles": [ "\\odot B lieson A C D" ], "semantics": [ "DC = 1.5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3336.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "Z", "X", "Y", "S", "A" ], "lines": [ "line W S Y", "line Z S X" ], "circles": [ "\\odot A lieson Z W X Y" ], "semantics": [ "WS = x", "XS = x+2", "ZS = x+6", "YS = x+12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3341.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", 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"PGDP/printed/image/PGDP10K_new_3351.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D C", "line A B C", "line A D", "line D B" ], "circles": [], "semantics": [ "DC \\perp AD on D", "AC \\perp DB on B", "DC = x", "DB = y", "CB = 9", "AC = 25" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3360.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "X", "V", "Y", "T", "U", "Z", "A", "B", "C", "D" ], "lines": [ "line V U Y", "line X Y", "line W T X", "line W V", "line \\ell lieson C V Z X B", "line m lieson A T Z U D", "line W Z Y" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3366.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "K", "M", "J" ], "lines": [ "line K J M", "line L M", "line L J", "line L K" ], "circles": [], "semantics": [ "LK = LJ = JM", "m \\angle MLJ = m \\angle 2", "m \\angle MJL = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3367.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "N", "L", "M" ], "lines": [ "line N M L", "line P L", "line P M", "line Q M", "line Q N" ], "circles": [], "semantics": [ "QM \\parallel PL", "NL \\perp QN on N", "NL \\perp PM on M" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3390.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K" ], "lines": [ "line J H D F", "line A C H K", "line \\ell lieson I H G", "line m lieson B C D E" ], "circles": [], "semantics": [ "m \\angle JHK = 5x", "m \\angle CHI = 2x", "m \\angle ACD = 5x+40" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3400.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line E F H", "line G H", "line C G", "line A C", "line A B", "line B E", "line D E", "line D H", "line D F" ], "circles": [], "semantics": [ "EH \\perp DF on F", "HG = 6", "DF = 3\\sqrt{3}" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3401.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B C", "line A B" ], "circles": [], "semantics": [ "BC \\perp AB on B", "BA = 1", "CB = \\sqrt{3}", "AC = 2", "m \\angle ACB = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3405.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C E", "line E D", "line A C D", "line A B" ], "circles": [], "semantics": [ "ED \\perp AD on D", "m \\angle CBA = 95", "m \\angle ECD = 40", "m \\angle CED = m \\angle 1", "m \\angle CAB = m \\angle 3", "m \\angle BCA = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3412.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "G", "I" ], "lines": [ "line D I", "line I G", "line D G" ], "circles": [ "\\odot I lieson G D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3422.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line A B", "line B C" ], "circles": [], "semantics": [ "BC = 7", "AB = x", "AC = 14.7", "m \\angle BCA = 18" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3423.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "E", "B", "F" ], "lines": [ "line C B", "line A B", "line A C", "line F E", "line D F", "line D E" ], "circles": [], "semantics": [ "CA = 3", "FE = 9", "CB = 6", "BA = 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3428.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "D", "G", "A", "B" ], "lines": [ "line F A D", "line E A G" ], "circles": [ "\\odot B lieson E F G D" ], "semantics": [ "m \\angle DAG = m \\angle 3", "m \\widehat DG = 74", "m \\widehat FE = 90" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3456.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B D C", "line A D E" ], "circles": [ "\\odot F lieson B A C E" ], "semantics": [ "AD = x", "BD = 7", "CD = 12", "ED = 14" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3458.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "S", "R", "T" ], "lines": [ "line Q S Q", "line Q T Q", "line Q R Q", "line T S", "line R T", "line R S" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3464.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A B C", "line D C E", "line G E F", "line B G H" ], "circles": [], "semantics": [ "m \\angle DCB = 3x+3", "m \\angle CEF = 2x+2", "m \\angle GBA = 4x+4", "m \\angle EGH = x+1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3465.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "H", "G", "L", "J" ], "lines": [ "line G L", "line K L", "line G J K", "line H G", "line H J L", "line H K" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3485.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line C D E", "line H E F", "line B H G", "line A B D" ], "circles": [], "semantics": [ "m \\angle HBA = 3x+2", "m \\angle DEF = 2x+1", "m \\angle BDC = x+5", "m \\angle EHG = 2x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3495.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A C", "line A B", "line B D", "line E D", "line F E", "line F G", "line G H", "line H C" ], "circles": [], "semantics": [ "EF = BD = DE = 5", "GH = AC = CH = 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3510.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "V", "T", "U" ], "lines": [ "line T S", "line T V", "line V U", "line T U", "line S U" ], "circles": [], "semantics": [ "TV \\parallel SU", "TS = TU = VU" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3517.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "C", "B", "D", "E" ], "lines": [ "line E F B C", "line A C", "line A D B", "line D C" ], "circles": [], "semantics": [ "AB \\perp DC on D", "m \\angle BCD = 5x-20", "m \\angle ACD = 3x-2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3533.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line B C D E", "line A B", "line A D F" ], "circles": [ "\\odot G lieson A C F E" ], "semantics": [ "BA = 12", "FD = 2", "BC = 6", "ED = 3", "AD = x", "CD = y" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3536.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line A B", "line C D", "line B D", "line A C" ], "circles": [], "semantics": [ "AB \\perp BD on B", "CD \\perp AC on C", "AB = 34", "BD = 22", "AD = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3542.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "L", "N", "M", "P", "Q", "R", "S" ], "lines": [ "line K N", "line P S N", "line P Q M", "line N M", "line L Q R", "line K S R", "line K L", "line L M" ], "circles": [], "semantics": [ "m \\angle SKL = m \\angle NKS = m \\angle QML = m \\angle QMN", "m \\angle QLK = m \\angle QLM = m \\angle KNS = m \\angle SNM" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3547.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "E", "F", "G" ], "lines": [ "line D A B E", "line F C B" ], "circles": [ "\\odot G lieson C B" ], "semantics": [ "m \\angle CBA = m \\angle 2", "m \\widehat BC = 146" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3550.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "E", "G" ], "lines": [ "line C G E", "line D E", "line D G", "line C D" ], "circles": [], "semantics": [ "CD = DE" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3554.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "F", "E", "A", "B" ], "lines": [ "line C A E", "line D A F", "line D C" ], "circles": [ "\\odot B lieson D E F C" ], "semantics": [ "m \\angle CDA = 40", "m \\widehat ED = 98" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3566.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "Z", "Y", "P" ], "lines": [ "line Z Y", "line X Y", "line Z X", "line Z P", "line X P", "line P Y" ], "circles": [], "semantics": [ "XY \\perp ZX on X", "m \\angle XYP = 20" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3585.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "M", "Q", "N", "P" ], "lines": [ "line M N P Q", "line L Q", "line L P", "line L N", "line M L" ], "circles": [], "semantics": [ "MN = PQ", "m \\angle NML = m \\angle PQL", "m \\angle PNL = m \\angle 2 = m \\angle NPL = m \\angle 3", "m \\angle MNL = m \\angle 1", "m \\angle QPL = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3611.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Y", "X", "W", "Z" ], "lines": [ "line X W", "line W Z", "line X Y", "line Y Z" ], "circles": [], "semantics": [ "XW \\perp WZ on W", "m \\angle XYZ = 120" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3620.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line B D", "line A B", "line A C" ], "circles": [], "semantics": [ "BA = 15", "AC = x+5y", "CD = 3x+3y", "DB = 2x+y" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3621.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "P", "C", "Q", "D", "E" ], "lines": [ "line D A B E", "line B C", "line B Q P" ], "circles": [ "\\odot Q lieson B C P" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3629.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line A B D", "line C B", "line C D" ], "circles": [], "semantics": [ "CA = 15", "AB = x", "DB = 7", "DC = 14", "m \\angle ACB = m \\angle BCD" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3632.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line \\ell lieson G F E", "line m lieson C B D", "line H F B A" ], "circles": [], "semantics": [ "m \\angle GFB = m \\angle 4 = m \\angle DBF = m \\angle 6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3652.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "N", "A", "B", "C", "D", "E" ], "lines": [ "line C R A", "line A N E", "line D B A" ], "circles": [], "semantics": [ "m \\angle RAB = x", "m \\angle NAB = 2x-75" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3654.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C" ], "lines": [ "line A B", "line D C B", "line A C", "line A D" ], "circles": [], "semantics": [ "DB \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3665.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line C F", "line A C", "line A B", "line E G", "line B E", "line F G", "line D F" ], "circles": [], "semantics": [ "FD = 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3672.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B C D", "line D E", "line F E", "line A F" ], "circles": [ "\\odot B lieson A C" ], "semantics": [ "DC = 4", "FA = 9", "EF = 12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3673.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "F", "G" ], "lines": [ "line C D", "line D F", "line G F", "line C G" ], "circles": [], "semantics": [ "CD = CG", "DF = GF", "m \\angle DCG = 67", "m \\angle DFG = 49" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3679.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "V", "W", "U", "X", "Z", "Y" ], "lines": [ "line U Z Y X", "line W X", "line V W", "line W Y", "line V Z", "line V U" ], "circles": [], "semantics": [ "VW \\parallel UX", "VW \\perp VZ on V", "VW \\perp WY on W", "UZ = YX", "VU = WX" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3705.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line A C", "line D C", "line B D", "line B C" ], "circles": [], "semantics": [ "DC \\perp BD on D", "BA \\perp AC on A", "DB = AC = 6", "BA = CD = p", "BC = m", "m \\angle DBC = 60", "m \\angle ABC = m \\angle DCB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3717.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "T", "R", "Q", "S", "A", "B", "C", "D" ], "lines": [ "line A Q B R", "line C S R" ], "circles": [ "\\odot D lieson T S B Q" ], "semantics": [ "m \\angle BRS = 71", "m \\widehat BS = 106" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3724.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "J", "K", "M", "N", "O" ], "lines": [ "line L O K", "line J M K", "line L N J", "line N O", "line O M", "line N M" ], "circles": [], "semantics": [ "MK = JM", "LO = OK", "NJ = LN" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3727.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "I", "F", "H", "G", "A", "B", "C" ], "lines": [ "line C F G", "line G H B", "line G I A" ], "circles": [], "semantics": [ "m \\angle FGH = 3x-3", "m \\angle HGI = m \\angle FGH = 4x-14" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3735.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line B C D", "line A D", "line A C" ], "circles": [], "semantics": [ "BA \\perp AD on A", "AC = CD", "m \\angle BCA = 40", "m \\angle ABC = y", "m \\angle CDA = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3744.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B C", "line A B" ], "circles": [], "semantics": [ "BA = h", "CB = 12", "m \\angle CAB = 42", "m \\angle ACB = 48" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3760.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J" ], "lines": [ "line A D", "line D J", "line I J", "line C I", "line C A", "line B E", "line E H", "line G H", "line F G", "line F B" ], "circles": [], "semantics": [ "m \\angle ADJ = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3767.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line B C F H", "line D C A", "line E F G" ], "circles": [], "semantics": [ "DA \\parallel EG", "m \\angle HFG = 2x-60", "m \\angle FCA = 60-2x", "m \\angle FCD = m \\angle 1", "m \\angle CFE = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3771.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C" ], "lines": [ "line A C", "line B C", "line D C", "line A D", "line A B" ], "circles": [], "semantics": [ "DC = BC", "m \\angle ACB = m \\angle ACD" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3775.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "U", "T", "W", "V", "S", "R", "P", "Q" ], "lines": [ "line W P", "line P Q", "line R Q", "line S R", "line T S", "line U T", "line U V", "line V W" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3776.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B C" ], "circles": [ "\\odot C lieson B A" ], "semantics": [ "CB = 3", "m \\angle BCA = 32" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3802.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line F E", "line B E", "line C D", "line A D" ], "circles": [], "semantics": [ "m \\angle CDA = m \\angle 2", "m \\angle FEB = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3805.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "M", "Z", "Y" ], "lines": [ "line M N", "line M Y", "line Y Z", "line N Z" ], "circles": [], "semantics": [ "ZN = 6", "NM = 4.5", "YZ = b", "m \\angle NMY = 50", "m \\angle MYZ = 150", "m \\angle YZN = c" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3829.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N" ], "lines": [ "line a lieson A D H L N", "line b lieson K J G H D B", "line c lieson E F G H I", "line r lieson C F J L M" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3835.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "E", "H", "A", "D", "B", "C", "F", "I", "J", "K", "L", "M" ], "lines": [ "line E A I", "line E B F", "line H C K", "line H D L", "line J E H G M" ], "circles": [], "semantics": [ "m \\angle BEH = 58", "m \\angle DHG = 61", "m \\angle AEB = 62", "m \\angle CHD = 59" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3841.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C A", "line B A", "line C B" ], "circles": [ "\\odot B lieson C A" ], "semantics": [ "AB = 6", "m major \\widehat CA = 240" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3844.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C", "line A B D" ], "circles": [ "\\odot E lieson B D C" ], "semantics": [ "AC = 13", "AB = 7", "DB = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3851.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "M", "P", "Q", "A", "B", "C" ], "lines": [ "line P A M", "line N B M", "line N C P", "line Q P", "line Q A", "line B Q", "line Q M", "line C Q", "line N Q" ], "circles": [], "semantics": [ "NM \\perp BQ on B", "NP \\perp CQ on C", "PM \\perp QA on A", "QA = 7", "PM = 48" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3881.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "P", "M", "N" ], "lines": [ "line M N P", "line M L", "line P L" ], "circles": [ "\\odot M lieson L N" ], "semantics": [ "PN = 2", "LP = 10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3888.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line A C", "line D C", "line D B", "line B C" ], "circles": [], "semantics": [ "CD = 14", "AC = 10", "BA = DB", "m \\angle ABC = m \\angle 1", "m \\angle DBC = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3895.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "V", "T", "S", "X", "Y" ], "lines": [ "line R S", "line X Y", "line V T", "line R X V", "line S Y T" ], "circles": [], "semantics": [ "RS \\parallel VT", "VT = 3", "RS = 6", "YT = XV", "RX = SY" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3902.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "B", "C", "D", "H", "G" ], "lines": [ "line H B", "line H G", "line H C", "line B G C", "line D H", "line F H", "line A F C", "line A D B", "line A H" ], "circles": [], "semantics": [ "FH \\perp AC on F", "DH \\perp AB on D", "HG \\perp BC on G", "AF = 24", "AH = 25", "BH = 11", "m \\angle HCG = 28", "m \\angle DBH = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3911.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "L", "K", "P", "M", "H" ], "lines": [ "line M H L", "line K J L", "line K P M", "line P H", "line J H", "line P J" ], "circles": [], "semantics": [ "PJ = x", "ML = 2.7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3913.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "P", "T", "S", "Q", "A", "B", "C", "D" ], "lines": [ "line A P Q R B", "line C S Q", "line D T Q" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3920.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line A C" ], "circles": [], "semantics": [ "AB \\perp CB on B", "BC = 4", "AC = h", "m \\angle ACB = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3935.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line A C" ], "circles": [], "semantics": [ "AB \\perp CB on B", "BC = 24", "AC = x", "m \\angle CAB = 61" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3936.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line B C", "line D C", "line A D B" ], "circles": [], "semantics": [ "DC \\perp AB on D", "AC \\perp BC on C", "AD = 24", "BD = 14" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3946.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "X", "Z", "Y" ], "lines": [ "line Z Y", "line X Y", "line W X", "line W Z" ], "circles": [], "semantics": [ "ZY = 28", "YX = 24", "m \\angle ZWX = 105" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3949.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B C", "line A F E", "line E D", "line C D" ], "circles": [ "\\odot B lieson A C", "\\odot F lieson A E" ], "semantics": [ "ED \\perp CD on D", "ED = CD = 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3963.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "C", "D", "O", "F", "G", "H", "I", "J" ], "lines": [ "line H E O", "line I A O C G", "line J B O D F" ], "circles": [], "semantics": [ "HO \\perp IG on O", "m \\angle EOD = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3969.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line D C", "line A D", "line A B" ], "circles": [], "semantics": [ "DA = 2x+7", "BC = x+9", "m \\angle DAB = 2y-5", "m \\angle CBA = 2y+21" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3975.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B" ], "lines": [ "line B A" ], "circles": [ "\\odot A lieson B" ], "semantics": [ "AB = 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3986.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "T", "R", "S" ], "lines": [ "line R S", "line R Q" ], "circles": [ "\\odot T lieson Q S" ], "semantics": [ "RS = 26", "QR = 3x+8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3992.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "E", "F", "G" ], "lines": [ "line B D F", "line G A B", "line B C E" ], "circles": [], "semantics": [ "m \\angle ABC = 55", "m \\angle DBA = m \\angle DBC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_3993.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "H", "E", "G", "F", "A", "B", "C", "I" ], "lines": [ "line A D E H B", "line C G E", "line I F E" ], "circles": [], "semantics": [ "AB \\perp CE on E", "m \\angle GEF = m \\angle DEF = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4003.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line E F", "line E D", "line C B", "line B A" ], "circles": [], "semantics": [ "m \\angle FED = m \\angle 7", "m \\angle CBA = m \\angle 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4018.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line B A", "line A D", "line C D" ], "circles": [], "semantics": [ "BC = 2x+4y", "BA = 21", "AD = 6y+\\frac{1}{2}x", "CD = 3x+3y" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4029.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "P" ], "lines": [ "line D C", "line A D", "line A B", "line B C" ], "circles": [ "\\odot P lieson A B C D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4030.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "Z", "Y", "N" ], "lines": [ "line Z Y", "line Z N", "line Y N X", "line Z X" ], "circles": [], "semantics": [ "ZY \\perp ZX on Z", "ZN \\perp YX on N", "YN = 2.5", "XN = 10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4031.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "M", "P", "Z", "A", "B", "C" ], "lines": [ "line F Z B", "line F P C", "line F M A", "line M Z", "line Z P" ], "circles": [], "semantics": [ "FA \\perp MZ on M", "FC \\perp ZP on P", "MZ = ZP", "m \\angle ZFM = x+9", "m \\angle ZFP = 2x-1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4039.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line B D", "line A B", "line A C" ], "circles": [], "semantics": [ "AC = BD" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4048.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "Q", "T", "P", "S", "V", "U" ], "lines": [ "line Q R", "line R S T", "line Q V U T", "line Q P", "line P U S", "line P V R" ], "circles": [], "semantics": [ "QT \\perp PR on V" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4060.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "E" ], "lines": [ "line B A", "line E C A", "line E D B", "line D C" ], "circles": [], "semantics": [ "m \\angle EDC = m \\angle 1", "m \\angle ECD = m \\angle 4", "m \\angle BDC = m \\angle 2", "m \\angle ACD = m \\angle 5", "m \\angle ABD = m \\angle 3", "m \\angle BAC = m \\angle 6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4064.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "F", "D", "B", "C" ], "lines": [ "line A D", "line A B", "line B C", "line D C", "line E D", "line F E", "line F A" ], "circles": [], "semantics": [ "FA = AB = FE = BC = ED = DC", "m \\angle DAB = m \\angle DAF = m \\angle ADE = m \\angle ADC = 70", "m \\angle EFA = m \\angle ABC = m \\angle DEF = m \\angle BCD = 110" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4075.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line A D G", "line E F G", "line E B A", "line A C F", "line B C D" ], "circles": [ "\\odot C lieson B A D F" ], "semantics": [ "GE = 20", "AF = 10", "BA = AD = EB = DG" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4096.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line A B", "line C B", "line D B", "line G E", "line E F" ], "circles": [], "semantics": [ "m \\angle CBD = m \\angle 2", "m \\angle ABD = m \\angle 1", "m \\angle GEF = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4100.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C E", "line A E", "line A C D", "line D E", "line B D", "line B A" ], "circles": [], "semantics": [ "AD = 9", "EB = 16" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4110.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B" ], "lines": [ "line C B", "line A D B", "line A C", "line C D" ], "circles": [], "semantics": [ "AB \\perp CD on D", "CB \\perp AC on C", "AC = 10", "m \\angle DAC = 40" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4111.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "G", "M", "H", "A", "B", "C", "D", "E", "F", "I", "J" ], "lines": [ "line K E I M", "line G B E H", "line J I D C", "line A B D F" ], "circles": [ "\\odot E lieson K A G C F M J H" ], "semantics": [ "GH \\perp AF on B", "KM \\perp JC on I", "AB = BD", "DI = IJ" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4116.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "M", "D", "N" ], "lines": [ "line A D", "line C N D", "line B C", "line B M A", "line M N" ], "circles": [], "semantics": [ "BC \\parallel AD", "BM = MA", "CN = ND" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4130.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B", "F" ], "lines": [ "line A F", "line B F", "line A B", "line F D", "line B D", "line B C", "line C D" ], "circles": [], "semantics": [ "BC = 4", "AF = 10", "CD = FD = FB = 6", "DB = BA = 9" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4133.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line A D", "line C D", "line C B" ], "circles": [], "semantics": [ "BA \\perp AD on A", "AD \\perp CD on D", "BA = 4", "AD = a", "CB = 3\\sqrt{2}", "DC = b", "m \\angle DCB = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4137.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "R", "S", "T" ], "lines": [ "line P Q", "line Q T R", "line R S", "line P T S" ], "circles": [], "semantics": [ "PQ = 18", "RS = 6", "PT = 15", "QT = 12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4141.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line G H J K", "line F E D C", "line I H E B", "line L J D A" ], "circles": [], "semantics": [ "IB \\parallel LA", "m \\angle DEB = 70", "m \\angle JHI = 85", "m \\angle HJD = m \\angle 1", "m \\angle EDA = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4148.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D" ], "lines": [ "line B C", "line C D", "line A D", "line B A" ], "circles": [], "semantics": [ "BC \\parallel AD", "BA = CD", "m \\angle CBA = 115" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4159.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line C B", "line A B" ], "circles": [], "semantics": [ "CB \\perp AB on B", "AC = x", "CB = 15", "m \\angle ACB = 70" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4165.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line C A", "line B C", "line C D", "line D A", "line B D" ], "circles": [ "\\odot D lieson B C A" ], "semantics": [ "\\Phi D = 16" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4171.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "D", "F", "C", "Z", "G", "H", "I", "J", "K", "L" ], "lines": [ "line I A Z D J", "line L B Z E H", "line G F Z C K" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4197.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "S", "T" ], "lines": [ "line C D", "line B T D", "line A B", "line A S C", "line S T" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4201.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C D E F", "line B F", "line A C", "line A B", "line B E", "line A D" ], "circles": [], "semantics": [ "CF \\perp AD on D", "CF \\perp BE on E", "AC = 13", "CD = FE = 5", "DE = 12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4214.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "S", "Q", "R", "A", "B", "C" ], "lines": [ "line A R Q", "line B P Q", "line C S Q" ], "circles": [], "semantics": [ "m \\angle RQP = 50", "m \\angle RQS = m \\angle PQS" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4215.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P" ], "lines": [ "line C E L N", "line I J K L M", "line H G F E D", "line A G J P", "line B F K O" ], "circles": [], "semantics": [ "HD \\perp AP on G", "HD \\perp BO on F", "CN \\perp HD on E", "EF = \\frac{1}{2}x-7", "FG = \\frac{1}{4}x+5", "KJ = \\frac{1}{3}y-6", "KL = JK = 66-\\frac{2}{3}y" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4218.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line B D F", "line E D A", "line C D G" ], "circles": [], "semantics": [ "m \\angle ADG = y", "m \\angle FDG = 2x", "m \\angle BDA = 56", "m \\angle FDE = 7x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4222.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D A", "line A B", "line B E", "line D E", "line D C B" ], "circles": [ "\\odot C lieson A B E D" ], "semantics": [ "m \\angle BED = m \\angle 3", "m \\angle ABE = m \\angle 2", "m \\angle ADE = m \\angle 4", "m \\angle DAB = m \\angle 1", "m \\widehat BA = 60", "m \\widehat BE = 80" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4229.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "C", "E", "F" ], "lines": [ "line A D", "line D F C", "line B C", "line A E B", "line E F" ], "circles": [], "semantics": [ "AD = x-1", "CB = 15", "EF = 2x+1", "AE = EB", "DF = FC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4234.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C D", "line E D", "line A E", "line A B", "line E C" ], "circles": [], "semantics": [ "BD \\perp EC on C", "EA = 32", "CD = 12", "m \\angle DEC = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4244.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line B D", "line D C", "line A C" ], "circles": [], "semantics": [ "m \\angle ACD = 2x+24", "m \\angle CDB = y+58", "m \\angle ABD = 3x-17", "m \\angle BAC = 5y-6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4250.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line B C", "line A C" ], "circles": [], "semantics": [ "BA \\perp BC on B", "BC = x", "CA = 9.7", "m \\angle ACB = 17" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4253.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "F", "C", "E", "G", "D", "H", "I" ], "lines": [ "line B F C E", "line D E", "line F I H D", "line H E", "line A G I C", "line A B", "line G B" ], "circles": [], "semantics": [ "AC \\perp GB on G", "BE \\perp AB on B", "FD \\perp HE on H", "BE \\perp DE on E", "FC = 2", "EC = 1", "BF = 4", "BG = 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4263.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "F", "E", "A", "B", "G" ], "lines": [ "line A D E F B", "line E C G" ], "circles": [], "semantics": [ "m \\angle DEC = 11x-12", "m \\angle FEC = 2x+10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4266.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B E", "line E D", "line C D", "line B D", "line A C" ], "circles": [], "semantics": [ "AE \\perp ED on E", "AB = 22", "BE = 18", "m \\angle EDB = 40" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4269.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line D C", "line A D", "line B D", "line A B C", "line E F", "line F G", "line E H G", "line H F" ], "circles": [], "semantics": [ "DA = 21", "FG = x+4", "DC = 3x-6", "EF = 14", "AB = BC", "EH = HG", "m \\angle DAB = m \\angle FEH", "m \\angle DCB = m \\angle HGF" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4271.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C" ], "lines": [ "line D C", "line B C", "line A B", "line A D" ], "circles": [], "semantics": [ "DC = 12", "CB = 18", "m \\angle DAB = 115" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4282.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line n lieson B C D", "line m lieson A C E" ], "circles": [], "semantics": [ "line n \\perp line m on C" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4290.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "Q", "S", "T" ], "lines": [ "line Q S", "line R Q", "line R S", "line Q T", "line T S" ], "circles": [], "semantics": [ "m \\angle QRS = m \\angle QTS" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4291.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line C A", "line B C" ], "circles": [], "semantics": [ "CA \\perp BC on C", "CB = 5", "AC = 8", "m \\angle ABC = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4292.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "E", "F", "G", "H", "I", "J", "K" ], "lines": [ "line G A F D K", "line H B F E I", "line F C J" ], "circles": [], "semantics": [ "m \\angle EFA = 12y-10", "m \\angle CFD = 3x", "m \\angle CFB = 6x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4295.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A D F", "line B A", "line B E", "line E F", "line E D", "line A C E", "line B C" ], "circles": [], "semantics": [ "AE \\perp BC on C", "AF \\perp ED on D", "CB = DE = 5", "AF = 12", "AE = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4306.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line A D", "line D E", "line B E", "line A C E", "line B C D" ], "circles": [], "semantics": [ "BC = CD = 8", "AE = 17" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4307.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D A", "line B A", "line B C", "line A C" ], "circles": [], "semantics": [ "BC \\perp AC on C", "CA = x", "AB = 580", "m \\angle DAB = 27" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4308.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "T", "S", "V", "U", "W" ], "lines": [ "line T W S", "line R V S", "line T U R", "line U V", "line W V" ], "circles": [], "semantics": [ "WV = WS", "m \\angle VRU = m \\angle SVW" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4334.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line C F E D", "line a lieson B E H", "line b lieson A F G" ], "circles": [], "semantics": [ "m \\angle DEB = m \\angle 2", "m \\angle AFC = m \\angle 8", "m \\angle FEH = m \\angle 4", "m \\angle EFA = m \\angle 7", "m \\angle GFE = m \\angle 6", "m \\angle FEB = m \\angle 3", "m \\angle GFC = m \\angle 5", "m \\angle DEH = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4343.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B C", "line E C", "line D E", "line D A", "line D B" ], "circles": [], "semantics": [ "AC \\perp DA on A", "DA = 36", "AB = 27", "BC = 40" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4358.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line B A", "line A D", "line C D", "line B C", "line F E", "line E H", "line G H", "line F G" ], "circles": [], "semantics": [ "FG = x", "BC = 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4366.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "P", "Q", "R", "A", "B" ], "lines": [ "line P A R", "line N A Q" ], "circles": [ "\\odot B lieson N P Q R" ], "semantics": [ "m \\angle NAP = 51", "m \\widehat NP = 74" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4370.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "E", "D", "B" ], "lines": [ "line C B A", "line C D E", "line A E", "line B D" ], "circles": [], "semantics": [ "BD \\parallel AE", "m \\angle CBD = m \\angle 1", "m \\angle CDB = m \\angle 2", "m \\angle BAE = m \\angle 4", "m \\angle DEA = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4371.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line C A" ], "circles": [], "semantics": [ "AB \\perp CA on A", "AC = AB = 20", "BC = x", "m \\angle ABC = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4374.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "D", "C" ], "lines": [ "line A E", "line E D", "line A D", "line B A", "line B C", "line C D", "line A C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4384.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A D", "line E D", "line B E", "line B A", "line A C E", "line B C D" ], "circles": [], "semantics": [ "AE \\perp BD on C", "AC = BC = 4", "CD = 10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4389.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "R", "U", "T", "V", "S", "W", "A", "B", "C", "D", "E", "F" ], "lines": [ "line D Q V U F", "line E P V W S B", "line C R W T A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4402.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "L", "J", "A", "B", "C" ], "lines": [ "line A J K C", "line K L", "line B J L" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4404.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "R", "U", "T", "P" ], "lines": [ "line U T", "line T S", "line U R", "line R S" ], "circles": [ "\\odot P lieson U T S R" ], "semantics": [ "m \\angle UTS = 7y", "m \\angle TUR = 3x-5", "m \\angle URS = 11y", "m \\angle TSR = 3x+5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4436.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E" ], "lines": [ "line D C", "line A D", "line A B", "line B C", "line A E C", "line B E D" ], "circles": [], "semantics": [ "AB \\parallel DC", "AE = BE", "m \\angle BAE = m \\angle ABE = m \\angle DAE = m \\angle CBE", "m \\angle ADE = m \\angle BCE = m \\angle CDE = m \\angle DCE" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4443.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "G", "F" ], "lines": [ "line G F", "line D F", "line D G" ], "circles": [], "semantics": [ "DG = 15", "GF = 19", "FD = x", "m \\angle DGF = 125" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4448.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C", "line A B", "line B E", "line C D E", "line A D" ], "circles": [], "semantics": [ "CE \\perp AD on D", "BE \\perp CE on E", "BE = AD = 3", "CA = x", "CD = 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4452.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C D", "line A D", "line B A", "line C A" ], "circles": [], "semantics": [ "AD \\perp BA on A", "BD \\perp CA on C", "AB = y", "BC = 3", "AD = z", "AC = x", "CD = 12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4463.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "K", "L", "M" ], "lines": [ "line M L", "line K L", "line J K", "line J M", "line K M" ], "circles": [], "semantics": [ "m \\angle LKM = m \\angle JMK", "m \\angle JKM = m \\angle LMK" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4485.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "C", "G", "H", "B", "K", "A" ], "lines": [ "line G A H", "line J B H", "line J C G", "line K G", "line K H", "line C K", "line J K", "line B K", "line K A" ], "circles": [], "semantics": [ "JH \\perp BK on B", "JG \\perp CK on C", "GH \\perp KA on A", "JC = 4", "KJ = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4490.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "H", "N", "J", "P", "M", "A", "B", "C" ], "lines": [ "line G A C P", "line G M J", "line H P J", "line G N H", "line N A B J", "line H C B M" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4498.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line s lieson G F E", "line q lieson B C F H", "line r lieson A C D" ], "circles": [], "semantics": [ "line r \\parallel line s", "m \\angle BCA = m \\angle 1", "m \\angle HFG = m \\angle 6", "m \\angle FCA = m \\angle 8", "m \\angle GFC = m \\angle 7", "m \\angle FCD = m \\angle 3", "m \\angle HFE = m \\angle 5", "m \\angle CFE = m \\angle 4", "m \\angle BCD = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4505.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "E", "Z", "D", "X", "Y", "F", "G" ], "lines": [ "line C Z G F", "line A D C", "line C E B", "line D G Y B", "line A F B", "line A X G E" ], "circles": [ "\\odot G lieson D X F Y E Z" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4512.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A C F G", "line m lieson D C B", "line n lieson E F H" ], "circles": [], "semantics": [ "m \\angle CFE = 2x+45", "m \\angle ACB = 3x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4519.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line A B C", "line D C", "line B D" ], "circles": [], "semantics": [ "AD \\perp AC on A", "BD = BC", "m \\angle BCD = n", "m \\angle CBD = 126", "m \\angle ADB = m" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4533.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "U", "R", "V", "T", "S", "A", "B", "C", "D", "E", "F" ], "lines": [ "line m lieson A S U E", "line n lieson B T V D", "line l lieson F R S T C" ], "circles": [], "semantics": [ "m \\angle USR = 8x+4", "m \\angle STV = 9x-11" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4541.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "T", "N", "R", "S", "Q", "A", "B" ], "lines": [ "line N Q S", "line R S", "line T Q R", "line N T", "line \\ell lieson A Q B" ], "circles": [], "semantics": [ "m \\angle QNT = m \\angle QSR" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4556.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "Y", "Z" ], "lines": [ "line X Y", "line Y Z", "line X Z" ], "circles": [], "semantics": [ "XY \\perp YZ on Y", "XY = 15", "ZX = 25" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4566.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E" ], "lines": [ "line A B", "line B C", "line C D", "line A D" ], "circles": [ "\\odot E lieson A B C D" ], "semantics": [ "m \\angle CDA = 2y+16", "m \\angle ABC = 3y+4", "m \\angle BCD = 2x", "m \\angle DAB = 58" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4579.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "T", "P", "R", "Q", "S", "U" ], "lines": [ "line P T R", "line P S Q", "line R U Q", "line S U", "line T U", "line T S" ], "circles": [], "semantics": [ "PS = SQ", "RU = UQ", "PT = TR" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4584.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A D", "line A B", "line B C", "line E D C" ], "circles": [], "semantics": [ "m \\angle ADE = 110", "m \\angle ADC = z", "m \\angle DAB = y", "m \\angle ABC = 100", "m \\angle BCD = 87" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4589.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "K", "J", "P", "M", "Q", "A", "B", "C", "D", "E", "F", "G", "H", "I", "N" ], "lines": [ "line A J K L H", "line B M P Q I", "line C J M D", "line F K P E", "line G L Q N" ], "circles": [], "semantics": [ "CD \\parallel FE \\parallel GN", "KL = 4x+3", "MP = 3y+8", "PQ = MP = 5y-7", "JK = 6x-5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4590.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P" ], "lines": [ "line C D E F", "line G H I J", "line K L M N", "line A D H L O", "line B E I M P" ], "circles": [], "semantics": [ "CF \\parallel GJ \\parallel KN", "HL = 6", "DH = 4", "EI = 5", "MI = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4595.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "E", "F" ], "lines": [ "line B C", "line D C", "line F C", "line E B", "line A B", "line A E F D" ], "circles": [], "semantics": [ "AD \\parallel BC", "EB \\perp AD on E", "FC \\perp AD on F", "CF = 7", "AD = 27", "DC = AB", "m \\angle ABC = 135", "m \\angle EBA = m \\angle CBE" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4597.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "M", "P", "Q" ], "lines": [ "line N P", "line M Q P", "line M N", "line N Q" ], "circles": [], "semantics": [ "NP \\perp MN on N", "MP \\perp NQ on Q", "MQ = 15", "NQ = 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4610.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "J", "C" ], "lines": [ "line C J A", "line C B", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4637.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B C", "line A F", "line F E", "line D E", "line C D" ], "circles": [ "\\odot B lieson A C" ], "semantics": [ "AC \\perp AF on A", "AC \\perp CD on C", "CA = 10", "AF = 13", "ED = FE = 9" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4645.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "H", "E", "B", "G", "A", "D", "C" ], "lines": [ "line B A", "line A D", "line C D", "line B C", "line E F", "line E H", "line H G", "line F G" ], "circles": [], "semantics": [ "EF = 8", "HG = 5", "BA = x+1", "DC = x-1", "m \\angle HEF = m \\angle BAD", "m \\angle EFG = m \\angle CBA", "m \\angle BCD = m \\angle HGF", "m \\angle GHE = m \\angle ADC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4658.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "E", "D", "B", "F" ], "lines": [ "line A B D", "line A C E" ], "circles": [ "\\odot F lieson D E C B" ], "semantics": [ "AC = 7.5", "AB = 5", "EC = 4.5", "DB = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4682.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line E C B", "line E D A", "line D C" ], "circles": [], "semantics": [ "EA \\perp DC on D", "AB \\perp EA on A", "AD = 18", "ED = 8", "BC = x", "EC = 10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4685.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B" ], "lines": [ "line A C", "line A D B", "line C D", "line C B" ], "circles": [], "semantics": [ "AB \\perp CD on D", "BD = 3", "AD = 12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4697.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line B C D", "line A B" ], "circles": [ "\\odot B lieson A C" ], "semantics": [ "AD \\perp AB on A", "BA = BC = x", "DC = 10", "AD = 14" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4699.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C B", "line C A", "line A B" ], "circles": [], "semantics": [ "CB \\perp AB on B", "AB = 6", "BC = y", "CA = x", "m \\angle BCA = 37" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4704.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D" ], "lines": [ "line B A", "line B C", "line A D C" ], "circles": [ "\\odot A lieson B D" ], "semantics": [ "BC = 16", "AB = AD = r", "CD = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4710.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line E D B", "line A C E", "line C D" ], "circles": [], "semantics": [ "AB = 17", "CD = x-4", "AC = CE", "ED = DB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4732.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line A C", "line B C", "line A B", "line A D", "line D C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4750.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line A B", "line B D", "line C D" ], "circles": [], "semantics": [ "AC \\perp AB on A", "AB \\perp BD on B", "AC \\perp CD on C", "BD \\perp CD on D", "AB = CD = 5.7", "BD = AC = 1.8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4754.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line A D F G", "line E F", "line E D", "line C D B", "line C A", "line A B" ], "circles": [], "semantics": [ "m \\angle GFE = 136", "m \\angle DCA = 63", "m \\angle CDE = 69", "m \\angle EDF = 47", "m \\angle ADC = m \\angle 1", "m \\angle DEF = m \\angle 7", "m \\angle EFD = m \\angle 6", "m \\angle CAD = m \\angle 2", "m \\angle BAD = m \\angle 5", "m \\angle ABD = m \\angle 4", "m \\angle ADB = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4756.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "T", "S", "R" ], "lines": [ "line S T", "line P R T", "line P Q", "line Q R S" ], "circles": [], "semantics": [ "PT \\perp QS on R", "QR = RS", "PR = RT" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4780.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "E", "G", "F" ], "lines": [ "line G E", "line E F", "line G F", "line H G", "line H E" ], "circles": [], "semantics": [ "HE = GE" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4787.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C", "E", "F", "G" ], "lines": [ "line A C F", "line E B A" ], "circles": [ "\\odot G lieson B D C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4792.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line \\ell lieson A D B C" ], "circles": [ "\\odot E lieson D B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4795.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C D", "line B C E" ], "circles": [], "semantics": [ "m \\angle DCE = m \\angle 2", "m \\angle ACB = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4796.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "T", "R", "X", "S" ], "lines": [ "line T S X", "line W S R", "line W X", "line T R" ], "circles": [], "semantics": [ "TS = SR", "WS = SX", "m \\angle XSW = m \\angle TSR" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4797.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line B C", "line A C" ], "circles": [], "semantics": [ "BC = AC", "m \\angle BCA = 40", "m \\angle BAC = y", "m \\angle ABC = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4798.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "G", "N", "Q", "M", "T" ], "lines": [ "line L G", "line G T", "line L T", "line M N", "line N Q", "line M Q" ], "circles": [], "semantics": [ "LT = MQ", "m \\angle NMQ = m \\angle GLT" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4799.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B C", "line B A" ], "circles": [], "semantics": [ "BC \\perp BA on B", "BA = y", "CB = x", "AC = 17", "m \\angle BAC = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4802.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "J", "I", "V", "T", "U" ], "lines": [ "line H I J", "line T U V" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4805.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "V", "U", "T", "Q", "S", "W", "A", "R", "B", "C", "D", "A0", "A1" ], "lines": [ "line U B A R W", "line V Q A D S", "line A C T" ], "circles": [ "\\odot A0 lieson B Q R D C", "\\odot A1 lieson U V W S T" ], "semantics": [ "AR = RW", "m \\angle BAC = m \\angle DAC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4806.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "P", "Q", "R", "A" ], "lines": [ "line S R Q", "line P Q" ], "circles": [ "\\odot A lieson P R S" ], "semantics": [ "QR = x", "QP = 8", "SR = 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4819.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "N", "L", "M", "R", "P", "Q" ], "lines": [ "line L N K", "line N Q M", "line M P K", "line L R M", "line R Q P" ], "circles": [], "semantics": [ "LK \\perp NM on N", "MK \\perp LM on M" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4844.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P" ], "lines": [ "line F L", "line N J", "line O P", "line A B", "line C D", "line G I", "line E A", "line K O", "line B F", "line E K", "line M N", "line I M", "line D H", "line G C", "line H J", "line P L" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4847.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "C", "D", "F" ], "lines": [ "line A F C", "line B C", "line A B", "line A D", "line A E", "line E D C", "line B F D" ], "circles": [], "semantics": [ "AE \\perp EC on E", "AE = 24", "BF = DF = 15", "AF = CF = 20", "CD = 25" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4862.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line C H L", "line J K L", "line A D J", "line A B C", "line D F E", "line G I H" ], "circles": [ "\\odot I lieson G H K", "\\odot F lieson D B E" ], "semantics": [ "DE = GH = 4", "JL = CL = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4872.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "H", "J", "K", "L" ], "lines": [ "line L J", "line G K J", "line H K L" ], "circles": [ "\\odot L lieson G H J" ], "semantics": [ "GJ \\perp HL on K" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4878.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line E F", "line C A", "line B D", "line B C", "line D E" ], "circles": [ "\\odot G lieson A F" ], "semantics": [ "BD = DE = 13", "AF = 30", "CA = EF" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4883.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "T", "N", "S", "I", "E", "G", "L" ], "lines": [ "line H I", "line I S", "line T S", "line H T", "line E N", "line N G", "line L G", "line E L" ], "circles": 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"plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line A B", "line B C" ], "circles": [], "semantics": [ "AB \\perp BC on B", "CA = x", "CB = 19.5", "m \\angle BAC = m \\angle ACB = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4930.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "R", "Q", "S" ], "lines": [ "line P S", "line R S", "line Q R", "line Q P" ], "circles": [], "semantics": [ "RS = QP", "PS = QR" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4932.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "C", "D", "L", "M", "G", "J", "E", "F", "K" ], "lines": [ "line C D", "line D F K", "line H J K", "line C H", "line E F G", "line G M", "line L M", "line E J L" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4953.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D A", "line D B", "line A B", "line B C", "line D C" ], "circles": [], "semantics": [ "AD = BC = 12", "AB = x+3", "CD = 3x+1", "m \\angle ADB = 45", "m \\angle DBC = 115" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4965.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "V", "S", "R", "T" ], "lines": [ "line V T S", "line Q R S", "line Q V", "line R T" ], "circles": [], "semantics": [ "VS \\perp RT on T", "VS \\perp QV on V", "VQ = 5", "ST = 12", "TR = 3", "VS = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4966.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C", "line D C", "line A D", "line A B", "line B E D", "line A E C" ], "circles": [], "semantics": [ "BC \\perp AB on B", "AE = 2x-1", "CE = 3y+5", "AD = AB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_4969.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C E", "line D E", "line A B D", "line B C" ], "circles": [], "semantics": [ "ED = 4x", "BC = 12", "BD = AB", "AC = CE" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5051.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "F", "C", "G", "O", "E" ], "lines": [ "line A G O B", "line C O D", "line A E C", "line F E G D", "line F A" ], "circles": [ "\\odot O lieson A F C B D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5054.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "E", "F" ], "lines": [ "line l lieson E A F D", "line B F C", "line A C", "line B A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5060.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "D", "C", "A" ], "lines": [ "line E C", "line A C", "line B C D", "line B A E" ], 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"category": "plane geometry", "points": [ "D", "F", "K", "C", "A", "E", "B", "G" ], "lines": [ "line K G E", "line G F", "line C K F D", "line E F", "line A E B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5087.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "C", "B", "D", "F" ], "lines": [ "line E F", "line D F", "line C F B", "line A D B", "line E D", "line A E C" ], "circles": [], "semantics": [ "DF \\perp CB on F", "ED \\perp AC on E", "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5093.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "A", "D", "B", "C", "E", "O" ], "lines": [ "line A E B", "line A C F", "line C B", "line A D", "line C E D", "line F B", "line B D" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5094.png", "style": "printed", "split": "test", "category": 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"PGDP/printed/image/PGDP10K_new_5452.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "O", "N", "A", "P", "D", "E", "C", "B", "F", "G", "H", "I", "J" ], "lines": [ "line M A B P O", "line C P", "line N D C E O", "line P E", "line D F P", "line G A D I", "line H B F C J" ], "circles": [], "semantics": [ "m \\angle FDA = m \\angle \\alpha", "m \\angle PCF = m \\angle \\beta" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5458.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "D", "A", "F", "B", "C", "G" ], "lines": [ "line B D F", "line A G F", "line E F", "line C G D", "line A C E", "line A B" ], "circles": [], "semantics": [ "BF \\perp AB on B", "BF \\perp CD on D", "m \\angle GAB = m \\angle 1", "m \\angle GFE = m \\angle 2", "m \\angle GCA = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5462.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "E", "C", "F" ], "lines": [ "line E B", "line C B", "line E C", "line A C", "line D C", "line D A" ], "circles": [], "semantics": [ "AC \\perp DC on C", "CB \\perp EC on C" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5472.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "E", "D" ], "lines": [ "line A D", "line C D B", "line A E B", "line D E", "line C A" ], "circles": [], "semantics": [ "CB \\perp CA on C", "AB \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5473.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B" ], "lines": [ "line D B", "line A B", "line C B", "line D C", "line D A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5476.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "F", "C", "E", "G", "O", "H", "I" ], "lines": [ "line C E", "line A G E", "line C F", "line C G H D", "line F E I D", "line A H I O B", "line C A" ], "circles": [ "\\odot O lieson A C E B D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5485.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "M", "N", "A", "O", "D" ], "lines": [ "line C D O", "line A O B", "line M O", "line M D N", "line N O" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5491.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line d lieson J G B E", "line a lieson C I G D", "line b lieson K A B H", "line c lieson F I A L" ], "circles": [], "semantics": [ "m \\angle GIA = m \\angle 1", "m \\angle BGI = m \\angle 3", "m \\angle GBH = m \\angle 4", "m \\angle BAI = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5495.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "F", "E", "G", "H" ], "lines": [ "line A E C", "line E G D", "line B C D H", "line F D", "line E F", "line F G C", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5502.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "M", "N", "B", "C", "D", "E", "F", "P", "O" ], "lines": [ "line M E O P F N", "line A P", "line A E B", "line C F D", "line C P" ], "circles": [ "\\odot O lieson M A C N D B" ], "semantics": [ "MN \\perp AB on E", "MN \\perp CD on F" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5511.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "F", "C", "E" ], "lines": [ "line A E D", "line E F", "line C E B", "line A F B", "line D B", "line C A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5513.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "O", "D", "E" ], "lines": [ "line O E", "line A O", "line C O", "line O B", "line D O" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5532.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "B", "C", "E", "D", "G", "O", "H" ], "lines": [ "line A O G D", "line C G", "line G B", "line A E H B", "line C D B", "line G H F", "line C O E F", "line C A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5537.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "C", "D", "P", "F" ], "lines": [ "line A P", "line A D C", "line P F B", "line C E B", "line A B" ], "circles": [ "\\odot C lieson D P F E" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5540.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "I", "E", "F" ], "lines": [ "line B E C", "line B I", "line B D", "line A I E D", "line I C", "line A C", "line D C", "line B A" ], "circles": [ "\\odot F lieson A C D B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5548.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "C", "A", "E", "B", "D", "O" ], "lines": [ "line E O", "line C O", "line A O B", "line O D", "line O F" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5552.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "M", "A", "D", "C", "F", "G", "H", "I" ], "lines": [ "line B E", "line D H", "line E F H", "line A H", "line G A D M F C", "line D I E", "line A B", "line B I M H" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5574.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "A", "B", "M", "N", "O" ], "lines": [ "line A O C", "line A M B", "line D O N 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"line E O" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5614.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "C", "B", "A", "O", "D", "G", "H" ], "lines": [ "line C D F", "line E O D", "line B E", "line E G H C", "line B H D A", "line C A", "line B C", "line B G O F" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5633.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "D", "A", "F", "E" ], "lines": [ "line A E B", "line A F C", "line E F D", "line B C D" ], "circles": [], "semantics": [ "AB \\perp ED on E" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5634.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "F", "E", "G", "H" ], "lines": [ "line D G E", "line F H E", "line A E", "line A H G C", "line B E C", "line D C", "line A F D", "line A B" ], "circles": [], "semantics": [ "BC \\perp AB on B", "FE \\perp AD on F", "BC \\perp DC on C" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5639.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "C", "B", "D" ], "lines": [ "line D E", "line C D", "line B C", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5665.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C" ], "lines": [ "line B C", "line A C", "line B A" ], "circles": [], "semantics": [ "m \\angle CAB = 105" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5666.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "F", "D", "B", "A", "O", "E" ], "lines": [ "line A E O B", "line C E D", "line F D", "line C B", "line C A F" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5675.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "Q", "E", "P", "C", "D" ], "lines": [ "line A E D C", "line B C Q", "line P D Q", "line P E", "line A P B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5678.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B" ], "lines": [ "line A D B", "line C B", "line C D", "line A C" ], "circles": [], "semantics": [ "AB \\perp CD on D" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5698.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A" ], "lines": [ "line A B C" ], "circles": [], "semantics": [ "AB = 16.7", "BC = 12.8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5703.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line E A B C D F" ], "circles": [], "semantics": [ "AB = 14\\frac{1}{4}", "BC = 12\\frac{3}{4}", "CD = 12\\frac{1}{4}" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5711.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "M", "Y" ], "lines": [ "line X M Y" ], "circles": [], "semantics": [ "MY = x", "XM = x^{2}-2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5715.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Z", "Y", "X" ], "lines": [ "line X Z Y" ], "circles": [], "semantics": [ "ZY = 3n", "XZ = 3(n+4)" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5719.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "R", "T", "S" ], "lines": [ "line Q T", "line Q R", "line R S", "line T S" ], "circles": [], "semantics": [ "RS = 6x+8", "TQ = \\frac{1}{2}(14x+8)" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5721.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B C D" ], "circles": [], "semantics": [ "CD = 9", "CB = CD = x+3", "AB = 7y-2", "DA = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5728.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "B", "A" ], "lines": [ "line A B C D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5744.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E", "F", "G" ], "lines": [ "line E A B", "line B C G", "line B D F" ], "circles": [], "semantics": [ "m \\angle ABD = 10x-51", "m \\angle CBD = 6x-11" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5747.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C E", "line D C B" ], "circles": [], "semantics": [ "m \\angle ACB = m \\angle 8", "m \\angle ACD = m \\angle 7", "m \\angle ECB = m \\angle 9", "m \\angle ECD = m \\angle 6" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5778.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line B C D", "line A C F H", "line E F G" ], "circles": [], "semantics": [ "BD \\parallel EG", "m \\angle CFG = 135", "m \\angle DCA = m \\angle 1", "m \\angle BCF = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5781.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A D H", "line F E D B", "line C E G" ], "circles": [], "semantics": [ "CG \\parallel AH", "m \\angle ADB = x", "m \\angle ADE = 67", "m \\angle FEG = y" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5785.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A C F H", "line B C D", "line E F G" ], "circles": [], "semantics": [ "BD \\parallel EG", "m \\angle ACD = 151", "m \\angle HFE = 2x+1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5789.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A C F H", "line k lieson E F G", "line j lieson B C D" ], "circles": [], "semantics": [ "line j \\parallel line k", "m \\angle FCD = 2x", "m \\angle CFG = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5790.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A C F H", "line k lieson E F G", "line j lieson B C D" ], "circles": [], "semantics": [ "line j \\parallel line k", "m \\angle FCB = 20x+2", "m \\angle CFE = 9x+4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5791.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A C F H", "line j lieson B C D", "line k lieson E F G" ], "circles": [], "semantics": [ "line j \\parallel line k", "m \\angle ACD = m \\angle HFG = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5792.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line C D E", "line A D F", "line B D G" ], "circles": [], "semantics": [ "CE \\perp BG on D", "m \\angle ADB = 26", "m \\angle CDF = 4y", "m \\angle EDA = x+10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5798.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "S", "Q", "A", "B", "C", "D", "E", "F" ], "lines": [ "line C R S D", "line B R Q F", "line A S E" ], "circles": [], "semantics": [ "BF \\parallel AE", "m \\angle CRQ = x", "m \\angle RSE = 118" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5808.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "U", "T", "S", "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line C D T U E", "line A D F", "line B T S G" ], "circles": [], "semantics": [ "AF \\parallel BG", "m \\angle TDA = 4x-14", "m \\angle DTS = 3x+12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5834.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line A C" ], "circles": [], "semantics": [ "AB = CB", "m \\angle ABC = x", "m \\angle BAC = 2x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5839.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line A B", "line A C" ], "circles": [], "semantics": [ "AB = AC", "m \\angle CBA = x", "m \\angle BAC = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5844.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line C B", "line A B" ], "circles": [], "semantics": [ "AB = BC", "m \\angle CAB = m \\angle ACB = x", "m \\angle CBA = 72" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5845.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line A B", "line B C" ], "circles": [], "semantics": [ "AC = 17", "BA = 2x+3", "m \\angle ABC = m \\angle ACB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5860.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line A B C", "line D E F G", "line B E", "line B F" ], "circles": [], "semantics": [ "AC \\parallel DG", "EB = FB", "m \\angle FEB = 58", "m \\angle CBF = m \\angle 1", "m \\angle EBF = m \\angle 2", "m \\angle DEB = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5863.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "T", "S" ], "lines": [ "line T S", "line R T", "line R S" ], "circles": [], "semantics": [ "RT = 8-4w", "RS = 2w+5", "m \\angle TRS = m \\angle STR = m \\angle TSR" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5865.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "E" ], "lines": [ "line A C E", "line B C D", "line D E", "line A B" ], "circles": [], "semantics": [ "AC = CB", "m \\angle CDE = 100", "m \\angle CAB = m \\angle CBA", "m \\angle ECD = m \\angle CED" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5894.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "Z", "Y", "W" ], "lines": [ "line X Z", "line Y W Z", "line X Y", "line X W" ], "circles": [], "semantics": [ "XY = 8", "XZ = 12.8", "ZW = t-2", "YW = \\frac{t}{2}", "m \\angle YXW = m \\angle ZXW" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5925.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "P", "Q", "R", "T" ], "lines": [ "line R P S", "line R T", "line S Q T", "line P Q" ], "circles": [], "semantics": [ "PQ = x+9", "RT = 4x-27" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5944.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "G", "H", "K", "A", "B" ], "lines": [ "line t lieson A G H B", "line G K", "line G J", "line J H K" ], "circles": [], "semantics": [ "line t \\perp JK on H" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5948.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "S", "O", "R", "T", "Q" ], "lines": [ "line R T Q", "line R S P", "line P Q", "line P O T", "line S O Q" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5968.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "F", "E", "G", "H", "J" ], "lines": [ "line D F", "line J H", "line G H", "line E F", "line J G", "line D E" ], "circles": [], "semantics": [ "DE = 15", "FE = 24", "JG = 2y+1", "HG = y^{2}-4y+3", "m \\angle FED = 126", "m \\angle HGJ = 12y+42" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5976.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "G", "E", "H" ], "lines": [ "line E G", "line F E", "line G H", "line E H", "line F G" ], "circles": [], "semantics": [ "m \\angle GEH = 36", "m \\angle EFG = 110", "m \\angle GHE = x+24" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5986.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "K", "L", "P", "N" ], "lines": [ "line M K P", "line M L N", "line P N", "line K L" ], "circles": [], "semantics": [ "KL \\parallel PN", "MK = 12", "ML = 9", "NL = x", "PK = x+1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_5991.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B E", "line C D E", "line A C", "line B D" ], "circles": [], "semantics": [ "AC \\parallel BD", "BA = 5", "BE = x", "CD = 4", "ED = 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6018.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "P", "K", "M", "T", "R", "N", "V" ], "lines": [ "line N K", "line G K", "line R P", "line R V", "line M G", "line M N", "line P T", "line V T" ], "circles": [], "semantics": [ "KG = 8.4", "GM = MN = 4", "PT = TV = 3", "RV = 6.3", "RP = x+4", "KN = 3x-2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6021.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line F G", "line B G", "line E H", "line A B", "line D H", "line A F", "line C E", "line C D" ], "circles": [], "semantics": [ "AB \\perp AF on A", "CE \\perp CD on C", "FG \\perp AF on F", "EH \\perp CE on E", "AB = AF = 8", "DC = CE = 6", "GB = 12", "HD = z", "m \\angle GBA = y", "m \\angle FGB = 42", "m \\angle EHD = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6025.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "X", "B", "C", "Y", "Z" ], "lines": [ "line A C", "line X Z", "line A B", "line X Y", "line B C", "line Y Z" ], "circles": [], "semantics": [ "AB \\perp BC on B", "XY \\perp YZ on Y", "AC = 4", "AB = 2", "ZX = 3", "XY = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6037.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "T", "V", "Q", "U", "R", "A" ], "lines": [ "line Q U R V", "line P A R", "line T V", "line P Q", "line T A U" ], "circles": [], "semantics": [ "PQ = UR = 60", "QU = 40", "VR = 20", "m \\angle URA = m \\angle RVT", "m \\angle UQP = m \\angle RUA" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6039.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "B", "R", "A", "C", "T" ], "lines": [ "line S T", "line R T", "line B C", "line R S", "line A C", "line A B" ], "circles": [], "semantics": [ "TS = 15", "CB = 10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6040.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "U", "V", "R", "T" ], "lines": [ "line R T", "line U V", "line R U S", "line S V T" ], "circles": [], "semantics": [ "US = 6", "VU = 9", "RU = 2", "TV = x", "SV = x+3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6045.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C D", "line B A", "line A D", "line A C" ], "circles": [], "semantics": [ "BA \\perp AD on A", "BD \\perp AC on C", "DC = x", "BC = 5", "AD = x+2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6046.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B C", "line D C", "line A D", "line B D" ], "circles": [], "semantics": [ "AC \\perp BD on B", "DC \\perp AD on D", "CB = 20", "AB = x", "DB = x+5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6049.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Z", "X", "P", "Y" ], "lines": [ "line X P Y", "line Z Y", "line Z X", "line Z P" ], "circles": [], "semantics": [ "XY \\perp ZP on P", "ZY \\perp ZX on Z" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6078.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A" ], "lines": [ "line A B", "line A C", "line C B" ], "circles": [], "semantics": [ "AC = b", "CB = a", "AB = c" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6084.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C" ], "lines": [ "line B A", "line B C", "line A C" ], "circles": [], "semantics": [ "BA = 19", "BC = a", "AC = 23", "m \\angle BAC = 54" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6086.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A" ], "lines": [ "line B A", "line B C", "line C A" ], "circles": [], "semantics": [ "BC \\perp CA on C", "CA = 20", "BA = 32" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6099.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line A B", "line A C", "line B C D" ], "circles": [], "semantics": [ "AC \\perp BD on C", "AD = b", "AC = a", "DC = d", "BC = c", "AB = 4\\sqrt{3}", "m \\angle ABC = 60", "m \\angle ADC = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6121.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line E D F", "line A B", "line A D", "line B F", "line D B", "line C D", "line A C", "line C E" ], "circles": [], "semantics": [ "AB \\perp AD on A", "BF \\perp DB on B", "CD \\perp AC on C", "EF \\perp CE on E", "EF = x", "FE = 4", "m \\angle ABD = m \\angle DAC = m \\angle DCE = m \\angle ADB = m \\angle ADC = m \\angle CDE = m \\angle FDB = m \\angle DFB" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6133.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "S", "U", "T" ], "lines": [ "line S U", "line U T", "line S T", "line R U", "line R S" ], "circles": [], "semantics": [ "UT = 9.4", "m \\angle USR = 49" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6134.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line B C", "line A C" ], "circles": [], "semantics": [ "BC = 7.2", "AB = AC", "m \\angle ABC = 51" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6145.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Y", "X", "Z" ], "lines": [ "line X Y", "line X Z", "line Y Z" ], "circles": [], "semantics": [ "YZ = 4.3", "XZ = 7.6", "m \\angle XYZ = 50" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6149.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "D", "F" ], "lines": [ "line D F", "line E D", "line E F" ], "circles": [], "semantics": [ "ED = 11.7", "m \\angle FDE = 47", "m \\angle DFE = 55" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6161.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line C D", "line B D", "line A C" ], "circles": [], "semantics": [ "m \\angle BAC = m \\angle ABD = 2x", "m \\angle DCA = m \\angle CDB = 110" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6177.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "B" ], "lines": [ "line C B", "line A B", "line D A", "line D C" ], "circles": [], "semantics": [ "AB = x+6", "CB = 2x+7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6204.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C D E", "line A C", "line B D", "line B E", "line A B" ], "circles": [], "semantics": [ "AB \\parallel CE", "AC \\parallel BD", "CE \\perp BE on E", "CA = 16", "BE = 14", "CD = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6228.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C", "line A E", "line C D E", "line C B", "line B D" ], "circles": [], "semantics": [ "CE \\perp BD on D", "BC = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6238.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "J", "M", "K", "A" ], "lines": [ "line M A K", "line H M", "line J K", "line J A", "line H J" ], "circles": [], "semantics": [ "MK \\perp JA on A", "HJ = 6", "MH = 10", "KM = 12" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6246.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B" ], "lines": [ "line A B" ], "circles": [ "\\odot B lieson A" ], "semantics": [ "BA = 4.2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6249.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line B C", "line A C" ], "circles": [ "\\odot C lieson A B" ], "semantics": [ "BC \\perp AC on C", "BC = 18" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6259.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "E", "D" ], "lines": [ "line A C D", "line E C B" ], "circles": [ "\\odot C lieson A B D E" ], "semantics": [ "DC = 8", "m \\angle ACB = m \\angle DCE = 125" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6262.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B" ], "lines": [ "line A C", "line B C" ], "circles": [ "\\odot C lieson A B" ], "semantics": [ "AC = 10", "m \\angle ACB = 70" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6274.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B C", "line A B" ], "circles": [ "\\odot B lieson A C" ], "semantics": [ "BC \\perp AB on B", "AB = 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6275.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line A C", "line B C" ], "circles": [ "\\odot B lieson A C", "\\odot D lieson A C B" ], "semantics": [ "AB \\perp BC on B", "AB = 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6288.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "S", "T" ], "lines": [ "line S T", "line R S" ], "circles": [ "\\odot S lieson R T" ], "semantics": [ "ST = 2", "m \\widehat RT = 47" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6289.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A" ], "lines": [ "line C A", "line B A", "line B C" ], "circles": [ "\\odot B lieson C A" ], "semantics": [ "CB = 10", "m \\angle CAB = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6322.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C E", "line D C B", "line A B", "line D E", "line A D", "line B E" ], "circles": [], "semantics": [ "m \\angle ECB = 63", "m \\angle CDE = 37", "m \\angle CAB = m \\angle 3", "m \\angle CBA = m \\angle 1", "m \\angle CED = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6330.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "G", "K", "J", "H" ], "lines": [ "line F K H", "line J K G", "line F G", "line J H", "line F J", "line G H" ], "circles": [], "semantics": [ "FJ \\parallel GH", "FG \\parallel JH", "FG = 5", "KG = 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6332.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line A B", "line B D", "line A C" ], "circles": [], "semantics": [ "m \\angle BAC = a", "m \\angle ABD = b", "m \\angle DCA = 101" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6338.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "L", "M", "K", "N" ], "lines": [ "line L K", "line M N", "line L M", "line K N" ], "circles": [], "semantics": [ "LK \\parallel MN", "LM \\parallel KN", "m \\angle KLM = 2s+30", "m \\angle LKN = 3s+50" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6346.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "G", "E", "H" ], "lines": [ "line E H", "line F G", "line F E", "line G H" ], "circles": [], "semantics": [ "m \\angle GFE = 9z+19", "m \\angle FGH = 14w-1", "m \\angle EHG = 11z-3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6356.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "A", "D" ], "lines": [ "line B E D", "line A E C", "line B C", "line A D", "line B A", "line C D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6357.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "X", "Y", "W", "Z" ], "lines": [ "line W Z", "line W X", "line X Y", "line Z Y" ], "circles": [], "semantics": [ "XW = b+6", "ZY = 5b-8", "m \\angle ZWX = 6a", "m \\angle WXY = 14a" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6361.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "R", "U", "S", "T" ], "lines": [ "line Q U T", "line S U R", "line Q R", "line S T", "line R T", "line Q S" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6369.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "N", "Q", "P" ], "lines": [ "line M N", "line Q P", "line N P", "line M Q" ], "circles": [], "semantics": [ "m \\angle NMQ = 2x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6370.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "K", "L", "N", "M" ], "lines": [ "line N M", "line K L", "line L M", "line K N" ], "circles": [], "semantics": [ "m \\angle MNK = x+40", "m \\angle NML = 2x-10" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6381.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "Y", "C", "D" ], "lines": [ "line D Y B", "line A D", "line A B", "line D C", "line B C", "line A Y C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6383.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "R", "P", "S" ], "lines": [ "line P R", "line Q R", "line Q P", "line R S", "line P S" ], "circles": [], "semantics": [ "m \\angle RQP = 104", "m \\angle PRQ = m \\angle 3", "m \\angle PRS = m \\angle 4", "m \\angle RPQ = m \\angle 1", "m \\angle RPS = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6391.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C D", "line A E", "line B C E", "line B D", "line E D", "line A B" ], "circles": [], "semantics": [ "m \\angle CDE = 35", "m \\angle CBD = m \\angle 2", "m \\angle ACB = m \\angle 1", "m \\angle ACE = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6398.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C D", "line E D", "line B A", "line B E", "line A D", "line A C E" ], "circles": [], "semantics": [ "m \\angle CDE = 3x+6", "m \\angle DEC = 8x+7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6399.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D C B", "line A C E", "line A D", "line A B", "line D E", "line B E" ], "circles": [], "semantics": [ "m \\angle CBE = 4x-12", "m \\angle CEB = 3x+4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6413.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line B D", "line A D", "line C D", "line A B" ], "circles": [], "semantics": [ "m \\angle ACD = 70", "m \\angle DAB = m \\angle 3", "m \\angle DBA = m \\angle 4", "m \\angle CAD = m \\angle 2", "m \\angle BDA = m \\angle 5", "m \\angle ADC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6414.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line B D", "line B A", "line A C", "line D C" ], "circles": [], "semantics": [ "m \\angle CBA = 27", "m \\angle BAC = m \\angle 1", "m \\angle BCA = m \\angle 2", "m \\angle BCD = m \\angle 3", "m \\angle CBD = m \\angle 5", "m \\angle BDC = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6422.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "R", "T", "S" ], "lines": [ "line T S", "line Q T", "line R S", "line Q R" ], "circles": [], "semantics": [ "QR = 12", "TS = 24", "m \\angle STQ = 52" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6433.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line D B", "line C A", "line C D" ], "circles": [], "semantics": [ "AC = 6x+1", "AB = 2y+6", "CD = AC = 3x+6", "DB = AB = 4y-3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6440.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "S", "U", "T" ], "lines": [ "line R S", "line S T", "line R U", "line U T" ], "circles": [], "semantics": [ "RS \\parallel UT", "RU = ST = 10", "m \\angle SRU = 65" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6456.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "Q", "X", "Y", "P", "S" ], "lines": [ "line P S", "line P X Q", "line X Y", "line Q R", "line R Y S" ], "circles": [], "semantics": [ "QR \\parallel PS", "XY = 22", "PS = 30", "YR = SY", "QX = PX" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6469.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "Q", "X", "Y", "P", "S" ], "lines": [ "line P S", "line P X Q", "line X Y", "line R Y S", "line Q R" ], "circles": [], "semantics": [ "QR \\parallel PS", "XY = 16", "RY = SY", "XQ = XP" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6471.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "J", "E", "G", "H" ], "lines": [ "line E J G", "line F G", "line H G", "line E H", "line F J H", "line E F" ], "circles": [], "semantics": [ "FE = EH", "FG = GH" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6477.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "G", "D", "C" ], "lines": [ "line A G C", "line D G B", "line A B", "line A D", "line B C", "line D C" ], "circles": [], "semantics": [ "AB \\parallel DC", "AD = BC" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6481.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "G", "I", "K", "J", "A" ], "lines": [ "line H K A", "line G K J", "line K I" ], "circles": [ "\\odot K lieson G H I J A" ], "semantics": [ "GJ \\perp KI on K", "m \\angle HKG = 23" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6484.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A C E", "line B C D" ], "circles": [ "\\odot F lieson B A D E" ], "semantics": [ "m \\angle ECB = m \\angle 6", "m \\widehat AB = 40", "m \\widehat ED = 35" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6495.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line B A" ], "circles": [ "\\odot B lieson A C" ], "semantics": [ "BA = 14", "m \\widehat AC = 45" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6499.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B" ], "circles": [ "\\odot B lieson A C" ], "semantics": [ "BA = 4", "m \\angle ABC = 110" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6504.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "B", "C", "D" ], "lines": [ "line B C A", "line D O", "line C O" ], "circles": [ "\\odot O lieson B A D" ], "semantics": [ "BA \\perp CO on C", "AB = 30", "CO = x", "DO = 17" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6510.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Y", "X", "O", "Z" ], "lines": [ "line Z X", "line Y X", "line Y O", "line O Z" ], "circles": [ "\\odot O lieson Y Z" ], "semantics": [ "m \\angle ZXY = 50" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6521.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "S", "Q", "R", "A", "B" ], "lines": [ "line Q A S", "line P A R", "line S R", "line P Q" ], "circles": [ "\\odot B lieson P S R Q" ], "semantics": [ "m \\angle AQP = 60" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6524.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A C F", "line B C D" ], "circles": [ "\\odot E lieson B A D F" ], "semantics": [ "BC = 6.5", "AC = 3", "DC = m", "FC = 7" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6534.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "P", "C", "A" ], "lines": [ "line B P A", "line P C" ], "circles": [ "\\odot P lieson B C A" ], "semantics": [ "m \\widehat AC = x", "m \\widehat BC = 2x-30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6555.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "L", "D" ], "lines": [ "line A B", "line A D" ], "circles": [ "\\odot L lieson B D" ], "semantics": [ "AB = x", "DA = 25" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6559.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B C", "line B D E" ], "circles": [ "\\odot D lieson B E" ], "semantics": [ "m \\angle CBD = x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6562.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "R", "C", "E", "F" ], "lines": [ "line E R B", "line C D A B" ], "circles": [ "\\odot F lieson D A R" ], "semantics": [ "m \\widehat RA = 60", "m major \\widehat DR = 190" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6567.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C A B", "line C D E" ], "circles": [ "\\odot F lieson A B E D" ], "semantics": [ "CD = x", "CA = x-5", "BC = 45", "CE = 36" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6571.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B C D", "line A C E" ], "circles": [ "\\odot F lieson B A D E" ], "semantics": [ "CA = 8", "CB = x", "DC = 2x", "CE = 9" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6572.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "R", "S", "T", "U", "A" ], "lines": [ "line R S", "line T U" ], "circles": [ "\\odot A lieson R S T U" ], "semantics": [ "l \\widehat SR = l \\widehat TU", "m \\widehat SR = 3x", "m \\widehat TU = 2x+27" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6581.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "H", "A", "B" ], "lines": [ "line A B" ], "circles": [ "\\odot A lieson G H B" ], "semantics": [ "AB = 6", "m \\widehat GH = 40" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6591.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "E", "A", "B", "F" ], "lines": [ "line C A F", "line B A E", "line D A" ], "circles": [ "\\odot A lieson C D E F B" ], "semantics": [ "CF \\perp DA on A", "m \\angle FAE = 62" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6594.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "U", "Q", "T", "P", "R", "S" ], "lines": [ "line S P Q", "line T P R", "line U P" ], "circles": [ "\\odot P lieson T U Q R S" ], "semantics": [ "m \\angle TPU = 40", "m \\angle QPR = 71" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6604.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "A", "E", "C", "D", "B" ], "lines": [ "line F A E B", "line C E D" ], "circles": [ "\\odot A lieson F D B C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6610.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "R", "Q", "S" ], "lines": [ "line P S", "line P R", "line S Q", "line R Q" ], "circles": [ "\\odot Q lieson R S" ], "semantics": [ "m \\angle SPR = x", "m \\angle SQR = 3x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6618.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "A", "E" ], "lines": [ "line C D A E", "line C B", "line B A" ], "circles": [ "\\odot A lieson D B E" ], "semantics": [ "BA = AD = EA = CD = 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6621.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "N", "L", "K", "A", "B" ], "lines": [ "line L A N", "line M A K", "line M N" ], "circles": [ "\\odot B lieson M N K L" ], "semantics": [ "m \\angle ANM = 43", "m \\widehat KN = 95" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6624.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "T", "S", "R", "A" ], "lines": [ "line Q T S", "line P T R", "line P Q", "line S R" ], "circles": [ "\\odot A lieson P Q R S" ], "semantics": [ "m \\widehat QR = 112", "m \\widehat PS = 84" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6626.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "J", "G", "H", "A" ], "lines": [ "line F A H", "line J H", "line F G", "line H G" ], "circles": [ "\\odot A lieson J F G H" ], "semantics": [ "m \\angle AHJ = 25" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6642.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "F", "E", "B", "G" ], "lines": [ "line B F C D", "line B A", "line A C E" ], "circles": [ "\\odot G lieson A D E F" ], "semantics": [ "m \\widehat AD = 82", "m \\widehat ED = 100", "m \\widehat EF = 120" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6644.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "H", "A", "F", "E", "G", "D", "B", "C", "I" ], "lines": [ "line A E G F", "line C D F", "line J E B", "line H F" ], "circles": [ "\\odot I lieson A J H G D C B" ], "semantics": [ "EA = FG = 4", "EG = 8", "FD = EB = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6647.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "Q", "P", "R", "T", "A" ], "lines": [ "line S P T", "line R P Q" ], "circles": [ "\\odot A lieson S Q T R" ], "semantics": [ "SP = 15", "QP = z", "PR = 10", "TP = 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6653.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "J", "K", "L" ], "lines": [ "line J K L" ], "circles": [], "semantics": [ "JL = 25", "KJ = 14" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6660.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line D E F", "line A E", "line B E", "line C E" ], "circles": [], "semantics": [ "m \\angle AEB = m \\angle 6", "m \\angle AEC = m \\angle 7", "m \\angle DEB = m \\angle 5", "m \\angle FEC = m \\angle 8" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6664.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line B C", "line C A" ], "circles": [], "semantics": [ "CD \\perp BC on C", "m \\angle BCA = 3x", "m \\angle ACD = 4x-15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6668.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "E", "F", "G" ], "lines": [ "line B C G", "line E A B", "line F D B" ], "circles": [], "semantics": [ "m \\angle ABD = \\frac{1}{2}x+20", "m \\angle CBD = 3x-85" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6679.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line H E C", "line G D A", "line B D E F" ], "circles": [], "semantics": [ "GA \\parallel HC", "m \\angle ADB = 5x", "m \\angle HEF = 176-3x" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6690.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K" ], "lines": [ "line D E F G H", "line A G K", "line C F J", "line B E I" ], "circles": [], "semantics": [ "BI \\parallel CJ \\parallel AK", "m \\angle GFJ = 3y", "m \\angle FEB = 5y-4", "m \\angle HGK = 2x+13" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6692.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line A C", "line C B" ], "circles": [], "semantics": [ "m \\angle ACB = x", "m \\angle BAC = 38", "m \\angle ABC = 44" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6702.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C B", "line A B", "line A C" ], "circles": [], "semantics": [ "AB = BC", "m \\angle BCA = 70" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6714.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "G", "F", "E", "B", "D" ], "lines": [ "line B E D", "line C F D", "line C G B", "line G F", "line G E", "line F E" ], "circles": [], "semantics": [ "CG = GB", "CF = DF", "BE = DE" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6717.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C B A", "line C D E", "line A E", "line B D" ], "circles": [], "semantics": [ "BD = 39", "EA = n^{2}-3", "BA = BC", "CD = ED" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6718.png", "style": "printed", "split": "test", "category": 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\\angle QPS = 100", "m \\angle BAD = 2x+4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6751.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C B A", "line C D", "line A D", "line B D" ], "circles": [], "semantics": [ "CD \\perp AD on D", "CA \\perp BD on B", "AB = 4", "CB = 21", "AD = x", "DB = y" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6752.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line B C D", "line A B", "line A C" ], "circles": [], "semantics": [ "AD \\perp AB on A", "BD \\perp AC on C", "AD = x", "AC = y", "BC = 3", "DC = 9" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6758.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C A", "line C D B", "line A B", "line A D" ], "circles": [], "semantics": [ "CB \\perp AD on D", "CA 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"PGDP/printed/image/PGDP10K_new_6796.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line A C", "line B D", "line A B" ], "circles": [], "semantics": [ "AB \\parallel CD", "AC = BD", "m \\angle CDB = 49", "m \\angle CAB = m \\angle 2", "m \\angle DBA = m \\angle 3", "m \\angle DCA = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6805.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C D", "line A B", "line E F", "line B D F", "line A C E" ], "circles": [], "semantics": [ "AB \\parallel EF", "AB = 18", "CD = x", "EF = 26", "AC = CE", "BD = FD" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6815.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "T", "M", "A", "B", "C", "D" ], "lines": [ "line S M C A D", "line S T B" ], "circles": [ "\\odot C lieson M T A" ], 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"C" ], "lines": [ "line B A", "line B C", "line A C" ], "circles": [], "semantics": [ "BC \\perp AC on C", "BA = 14", "AC = 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6895.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line a lieson H C F", "line c lieson D A C G", "line b lieson B A E" ], "circles": [], "semantics": [ "line c \\perp line b on A", "m \\angle HCA = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6896.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B", "O" ], "lines": [ "line D C", "line A O C", "line B C", "line B O D", "line A B", "line A D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6903.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J" ], "lines": [ "line J H D", "line F D A", 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"line D C" ], "circles": [ "\\odot O lieson A D B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6939.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "B", "E", "C", "D", "G" ], "lines": [ "line E G F", "line C F A", "line B D A", "line B E C" ], "circles": [ "\\odot G lieson E D F C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6953.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D" ], "lines": [ "line A D C", "line B C", "line B D", "line A B" ], "circles": [], "semantics": [ "AC \\perp BD on D" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_6954.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line b lieson B D", "line A B", "line a lieson A C" ], "circles": [], "semantics": [ "m \\angle DBA = m \\angle 2", "m \\angle BAC = m \\angle 1" ] }, { "diagram": 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"split": "test", "category": "plane geometry", "points": [ "M", "B", "A", "C", "D", "E", "F", "G", "H" ], "lines": [ "line b lieson F B M C", "line c lieson H A B E", "line A M", "line a lieson G A D" ], "circles": [], "semantics": [ "line b \\perp AM on M", "m \\angle BAM = m \\angle 2", "m \\angle HAD = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7032.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "C", "O" ], "lines": [ "line D A", "line D C O B", "line B A" ], "circles": [ "\\odot O lieson C A B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7034.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "F", "D" ], "lines": [ "line A E C", "line F D C", "line B C", "line F E", "line B D E", "line A F B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7045.png", "style": "printed", "split": "test", "category": 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"lines": [ "line C O", "line C E D", "line A O E B", "line A C" ], "circles": [ "\\odot O lieson A D B C" ], "semantics": [ "CD \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7068.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "O" ], "lines": [ "line D C", "line A O D", "line A C", "line A B", "line B C" ], "circles": [ "\\odot O lieson D C B A" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7069.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "B", "A", "C", "O", "D" ], "lines": [ "line E C B", "line F A B", "line F D C", "line E D A" ], "circles": [ "\\odot O lieson D C B A" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7094.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "O", "E" ], "lines": [ "line D C", "line A O E C", "line B C", "line B E D", "line A B" ], "circles": [ "\\odot O lieson A D C B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7103.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C B", "line E A", "line D C E", "line D B A" ], "circles": [], "semantics": [ "CB = 2", "DB = 6", "BA = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7106.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B", "O" ], "lines": [ "line A O B", "line D B", "line A D", "line C A", "line C D" ], "circles": [ "\\odot O lieson A B D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7109.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "O", "D" ], "lines": [ "line A C", "line B C", "line B D O A" ], "circles": [ "\\odot O lieson A C D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7111.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "O", "E", "F", "G" ], "lines": [ "line B C", "line A O B", "line E O F", "line G C D" ], "circles": [ "\\odot O lieson A E B C F" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7117.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "O", "D" ], "lines": [ "line A O D C", "line A B", "line B C" ], "circles": [ "\\odot O lieson A D B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7122.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "A", "D", "O", "B", "C", "G", "H" ], "lines": [ "line E B O A", "line B H C", "line G H", "line E G D", "line D F C" ], "circles": [ "\\odot O lieson B G F H A" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7134.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "O", "E", "F", "G" ], "lines": [ "line A C", "line A O B", "line D F A", "line G D C E" ], "circles": [ "\\odot O lieson A F C B" ], "semantics": [ "DA \\perp GE on D" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7144.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "A", "C", "B", "O" ], "lines": [ "line A P", "line A B", "line A O C", "line O B", "line B P" ], "circles": [ "\\odot O lieson A B C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7146.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "F", "B", "A", "G", "D", "K" ], "lines": [ "line A D", "line C G D", "line B F C", "line B E A" ], "circles": [ "\\odot K lieson F E G" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7147.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D" ], "lines": [ "line C B", "line C A", "line D C", "line D A", "line B A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7156.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "O" ], "lines": [ "line O B", "line O C A", "line B A", "line B C" ], "circles": [ "\\odot O lieson C B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7158.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "O", "D" ], "lines": [ "line A C", "line B O D C", "line B A" ], "circles": [ "\\odot O lieson B A D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7170.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "O" ], "lines": [ "line A O B", "line A D", "line C A", "line C D", "line D B" ], "circles": [ "\\odot O lieson A B D" ], "semantics": [ "m \\angle ACD = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7177.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "C", "D" ], "lines": [ "line A C", "line D E", "line B E C", "line B D A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7178.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "G", "F", "E", "C", "B" ], "lines": [ "line A E F G", "line D G", "line C F", "line B E", "line A B C D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7189.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "E", "F", "G", "H", "I" ], "lines": [ "line a lieson I C H", "line A E C", "line b lieson D F E G", "line B F A", "line B C" ], "circles": [], "semantics": [ "AC \\perp BC on C", "m \\angle DFB = m \\angle 2", "m \\angle HCE = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7191.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "O", "B", "A" ], "lines": [ "line D O", "line A O", "line A B", "line D C", "line C O", "line O B" ], "circles": [], "semantics": [ "m \\angle DOA = m \\angle \\alpha" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7197.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "C", "D", "A", "B", "E", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q" ], "lines": [ "line l_{1} lieson K A B I C Q", "line c lieson N F C O", "line l_{2} lieson L D E I F P", "line b lieson G B E J", "line a lieson M A D H" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7222.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "I" ], "lines": [ "line A C", "line B I", "line B C", "line A B", "line I C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7229.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "A", "B", "D", "E", "C", "O" ], "lines": [ "line E D", "line B C", "line A C", "line F A", "line A B", "line F E", "line D C" ], "circles": [ "\\odot O lieson A F E D C B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7233.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "B'", "A'", "A" ], "lines": [ "line A B", "line C B", "line C A B'", "line A' C", "line A' B'" ], "circles": [], "semantics": [ "AB \\perp CB' on A", "A'C \\perp A'B' on A'" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7234.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "A", "E", "D", "C", "G", "H" ], "lines": [ "line A G H C", "line F H D", "line B E D C", "line F G E", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7247.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "A", "F", "E" ], "lines": [ "line A F C", "line B D C", "line E D", "line D F", "line A E B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7254.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "O", "D", "B" ], "lines": [ "line C D", "line A O D", "line B A", "line B C" ], "circles": [ "\\odot O lieson A B C D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7259.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "E", "G", "F", "H", "I" ], "lines": [ "line C F D", "line I E F H", "line F G", "line A E G B" ], "circles": [], "semantics": [ "m \\angle IEG = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7269.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line A G C", "line l lieson I G F H", "line D E G", "line B E F C", "line D F", "line A B" ], "circles": [], "semantics": [ "m \\angle EFD = m \\angle 2", "m \\angle AGE = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7276.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "F", "E", "O" ], "lines": [ "line B E A", "line E F", "line B C", "line O E", "line C F A", "line O F" ], "circles": [ "\\odot O lieson B A C" ], "semantics": [ "CA \\perp OF on F", "BA \\perp OE on E" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7277.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "O", "E" ], "lines": [ "line A D", "line C O", "line C E D", "line A O E B" ], "circles": [ "\\odot O lieson A D B C" ], "semantics": [ "CD \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7280.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "O", "E" ], "lines": [ "line D E C", "line O C", "line A E O B", "line D A" ], "circles": [ "\\odot O lieson A D B C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7293.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B", "O" ], "lines": [ "line B C", "line A O", "line O C", "line B A", "line A D", "line D C" ], "circles": [ "\\odot O lieson B C D A" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7296.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "O", "E" ], "lines": [ "line D B", "line D E C", "line A O E B", "line O C" ], "circles": [ "\\odot O lieson A D B C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7317.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "E" ], "lines": [ "line C B", "line E B", "line D B", "line A B", "line E A", "line E D", "line D C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7321.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "F", "G", "E" ], "lines": [ "line A C", "line E F B", "line B C", "line B D G", "line A B", "line E G C", "line F D C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7323.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "A", "F", "D", "C", "O" ], "lines": [ "line D C", "line A O C", "line B F C", "line E O F", "line B O D", "line A B", "line A E D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7325.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "O" ], "lines": [ "line D O", "line D C", "line B C", "line A D", "line A B", "line O C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7337.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "N", "A", "E" ], "lines": [ "line D C", "line A C", "line B N C", "line A E B", "line A D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7341.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "Q", "D", "P" ], "lines": [ "line C D B", "line A B", "line Q P", "line A P D", "line C P", "line C Q A" ], "circles": [], "semantics": [ "CB \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7353.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line A E", "line A D", "line E C", "line D C" ], "circles": [ "\\odot F lieson A E B", "\\odot G lieson A B D", "\\odot H lieson B E C", "\\odot I lieson D B C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7354.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "O", "D", "C", "A", "E", "F", "G" ], "lines": [ "line O C", "line A O", "line O F E", "line B F C", "line D O", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7362.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "E", "F", "G", "H", "I" ], "lines": [ "line C E I B", "line A H F B", "line A D G C" ], "circles": [ "\\odot C lieson E G", "\\odot B lieson F I", "\\odot A lieson D H" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7369.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "C", "F", "E" ], "lines": [ "line A E F", "line B C F", "line D E C", "line A B", "line A D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7370.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "O" ], "lines": [ "line O C", "line B A", "line A O", "line B C" ], "circles": [ "\\odot O lieson B A C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7374.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "C", "A", "D", "B", "F", "G" ], "lines": [ "line C B", "line A E B", "line A G C", "line D F A", "line F G E", "line D C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7389.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "H", "O", "E" ], "lines": [ "line A C", "line A O E D", "line A H", "line B E H C", "line B A", "line B D" ], "circles": [ "\\odot O lieson A C D B" ], "semantics": [ "AH \\perp BC on H" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7390.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "G", "E", "D", "F" ], "lines": [ "line C E G B", "line A B", "line F G", "line D E", "line C D F A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7423.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "C", "D", "O" ], "lines": [ "line D E", "line A O C", "line B C E", "line B O D", "line D C", "line A B", "line A D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7442.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "O", "E", "D" ], "lines": [ "line A E C", "line D O", "line B C", "line O E", "line B D A", "line O C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7444.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "D", "A" ], "lines": [ "line D C", "line E C", "line B C", "line B E", "line A B", "line A E D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7445.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "E" ], "lines": [ "line C B", "line D E B", "line A B", "line E A", "line D A", "line D C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7450.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "E", "F" ], "lines": [ "line A C F", "line B C", "line A B E", "line B D", "line C D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7452.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "D", "C", "O", "F" ], "lines": [ "line D C", "line A O F C", "line B E C", "line B O D", "line A B", "line A D", "line O E", "line D F E" ], "circles": [], "semantics": [ "BD \\perp OE on O" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7498.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "O", "E" ], "lines": [ "line A E C", "line D O", "line E O", "line B O C", "line A D B" ], "circles": [ "\\odot O lieson B D E C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7564.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "E", "D", "F", "G" ], "lines": [ "line C D B", "line A E B", "line C E", "line G E D F", "line A C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7599.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "C", "O", "E", "F" ], "lines": [ "line A F D", "line B O", "line A E O", "line C D", "line C F E B" ], "circles": [ "\\odot O lieson C A B D" ], "semantics": [ "AO \\perp CB on E" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7608.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "O", "E" ], "lines": [ "line D O E C", "line O A", "line D B", "line B E A" ], "circles": [ "\\odot O lieson D A C B" ], "semantics": [ "m \\angle EOA = 30" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7622.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "A", "M", "C", "B", "D", "E", "F" ], "lines": [ "line a lieson E M C N F", "line D C", "line B M", "line A B", "line B C", "line A D", "line D N" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7642.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "O" ], "lines": [ "line B C", "line A D C", "line A O B", "line O D" ], "circles": [ "\\odot O lieson B C A" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7691.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "M", "O" ], "lines": [ "line B C", "line A O", "line M O", "line A M B", "line O C" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7693.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "B", "D", "G", "C", "E", "O", "H" ], "lines": [ "line F C E D", "line G H D", "line A O H E B", "line G C", "line A G F", "line A D" ], "circles": [ "\\odot O lieson A G C B D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7695.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "B", "A", "E", "O", "F", "G" ], "lines": [ "line C F E", "line A G O", "line O F B", "line C G D", "line A D", "line B E" ], "circles": [ "\\odot O lieson C B E D A" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7707.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "O" ], "lines": [ "line C D", "line B O", "line C B", "line A B", "line O D" ], "circles": [ "\\odot O lieson A B D C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7718.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "E", "M", "O" ], "lines": [ "line A E C", "line B D C", "line A O B", "line B M E", "line O M D" ], "circles": [ "\\odot O lieson A E D B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7725.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "E", "O" ], "lines": [ "line A O B", "line C D B", "line A E C", "line E B" ], "circles": [ "\\odot O lieson E A B D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7726.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "O", "E" ], "lines": [ "line C B", "line C E D", "line A O E B", "line A C", "line A D" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7733.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "O", "E" ], "lines": [ "line A C", "line A E D", "line B O E C", "line A O", "line B A", "line C D" ], "circles": [ "\\odot O lieson B A C D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7752.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "O", "A", "B", "C" ], "lines": [ "line Q O", "line l lieson B P A", "line O C P", "line Q P" ], "circles": [ "\\odot O lieson Q C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7758.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "F", "B", "H", "A", "C", "D", "O" ], "lines": [ "line H C B", "line D B", "line A O B", "line F D H E" ], "circles": [ "\\odot O lieson A D C B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7772.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "B", "A", "C" ], "lines": [ "line O B", "line O C", "line A O" ], "circles": [], "semantics": [ "m \\angle COA = m \\angle 2", "m \\angle BOC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7787.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "C", "D" ], "lines": [ "line A D C", "line D E", "line B E C", "line A B" ], "circles": [], "semantics": [ "DE \\perp BC on E" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7800.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "E", "O", "F", "G" ], "lines": [ "line E D", "line A G C", "line B G O", "line E F C", "line O F D", "line A B" ], "circles": [ "\\odot O lieson A E D C B" ], "semantics": [ "m \\angle DEF = 30", "m \\angle GAB = 25" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7801.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "O", "E" ], "lines": [ "line C B", "line D O", "line C E D", "line A E O B", "line A C" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7805.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line b lieson H B E", "line A F C", "line a lieson G F D", "line C B I" ], "circles": [], "semantics": [ "m \\angle CFG = m \\angle 1", "m \\angle FCB = m \\angle 2", "m \\angle HBI = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7824.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "D", "B", "A", "O", "C", "F" ], "lines": [ "line A F E", "line D F C", "line B O C E", "line A B", "line A D" ], "circles": [ "\\odot O lieson B A D E" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7841.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "V", "T", "U", "R", "S" ], "lines": [ "line U V", "line T S V", "line U S R", "line U T", "line V R" ], "circles": [], "semantics": [ "m \\angle SRV = m \\angle STU" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7855.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "T", "R", "U", "V", "S" ], "lines": [ "line R U", "line S U", "line S V", "line T S R", "line T V" ], "circles": [], "semantics": [ "TV = SU", "RU = SV" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7857.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "V", "T", "U", "S", "W" ], "lines": [ "line T W V", "line U W S", "line S V", "line T U" ], "circles": [], "semantics": [ "WS = TW", "UW = WV" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7879.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "U", "S", "R", "V", "T" ], "lines": [ "line U V", "line R T V", "line S T U", "line R S" ], "circles": [], "semantics": [ "m \\angle TRS = m \\angle UVT" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7880.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "T", "W", "U", "V", "X" ], "lines": [ "line V T W", "line X T", "line U X V", "line U W" ], "circles": [], "semantics": [ "m \\angle XUW = m \\angle TXV" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7884.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "F", "I", "G", "J" ], "lines": [ "line J H", "line J G", "line I G", "line I F", "line F G H" ], "circles": [], "semantics": [ "IF = JG", "JH = IG" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7886.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "W", "U", "V", "T", "X" ], "lines": [ "line V X T", "line V U", "line U X W", "line T W" ], "circles": [], "semantics": [ "VX = XW", "UX = XT" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7889.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "V", "S", "T", "U" ], "lines": [ "line U V", "line S V", "line S U", "line T S", "line T U" ], "circles": [], "semantics": [ "SV = TS", "UV = TU" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7890.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "S", "U", "W", "V", "T" ], "lines": [ "line U T S", "line V S", "line W T", "line U W", "line T V" ], "circles": [], "semantics": [ "WT = VS", "m \\angle TWU = m \\angle SVT" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7905.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "D", "P", "B", "C", "A", "E", "G", "O", "H", "I" ], "lines": [ "line P A G", "line P I H C", "line B O C", "line A H O D", "line E C D", "line F A I B" ], "circles": [], "semantics": [ "m \\angle HCO = m \\angle 4", "m \\angle HCE = m \\angle 3", "m \\angle GAH = m \\angle 2", "m \\angle GAF = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7919.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "P", "E", "F", "B", "A", "C" ], "lines": [ "line D C F", "line A B E", "line B C", "line A D", "line B P", "line C P" ], "circles": [], "semantics": [ "m \\angle CBP = m \\angle 3", "m \\angle BCP = m \\angle 4", "m \\angle ABC = m \\angle 1", "m \\angle DCB = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7940.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "N", "E", "H", "F", "C", "D", "M", "B" ], "lines": [ "line C M F", "line C H", "line C E", "line A H E N F B", "line E M", "line C A", "line C D", "line M N" ], "circles": [], "semantics": [ "CH \\perp AB on H", "CE \\perp EM on E" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7946.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "A_{2}", "D", "C", "A_{1}", "E", "F", "G" ], "lines": [ "line A_{1} G C", "line B C D", "line B F A_{1}", "line A F E C", "line B E G A_{2}", "line A B", "line C A_{2}" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7952.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "A'", "E", "D", "F" ], "lines": [ "line B D A", "line D E", "line D F A'", "line C F E A", "line B C", "line A' E" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7963.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "A", "D", "C", "B", "H", "G", "I", "J" ], "lines": [ "line E B F", "line H F", "line G A B I", "line E A H C", "line C F", "line J C D" ], "circles": [], "semantics": [ "m \\angle FBI = m \\angle 2", "m \\angle HFC = m \\angle 3", "m \\angle BFH = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7974.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "N", "B", "E", "C", "M", "F", "G" ], "lines": [ "line D C", "line F M N G", "line A N B", "line C B", "line A M E", "line E D" ], "circles": [], "semantics": [ "m \\angle NAM = 30", "m \\angle MNB = m \\angle 2", "m \\angle NME = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7981.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "G", "A", "E", "C", "B", "D", "H", "I", "J" ], "lines": [ "line E H D", "line F G", "line F I J E", "line A I B", "line A J H G", "line B C", "line D C" ], "circles": [], "semantics": [ "m \\angle EJH = m \\angle 2", "m \\angle DHJ = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7984.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "E", "F", "G" ], "lines": [ "line B A", "line C G A", "line B D C", "line E D G F" ], "circles": [], "semantics": [ "m \\angle AGD = m \\angle 2", "m \\angle BDG = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_7991.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "F", "E", "D", "G" ], "lines": [ "line A E C", "line F G C", "line B D", "line B G E", "line A F B", "line D C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8000.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "G", "N", "M", "E", "F", "C", "H" ], "lines": [ "line A D", "line A C E", "line F E", "line B H C F M D", "line A B", "line A H N G", "line M E G", "line D E N" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8003.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "Q", "P", "C", "D", "M", "A", "N", "B", "O", "E" ], "lines": [ "line M B O N", "line D E", "line A B", "line P A O Q", "line C E", "line F D A", "line C D", "line F C B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8006.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "O", "E", "F", "C", "B" ], "lines": [ "line A C F", "line C O", "line B C", "line A B E", "line B O" ], "circles": [], "semantics": [ "m \\angle EBO = m \\angle 3", "m \\angle ACB = m \\angle 4", "m \\angle CBA = m \\angle 1", "m \\angle FCO = m \\angle 6", "m \\angle CBO = m \\angle 2", "m \\angle OCB = m \\angle 5" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8018.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "F", "K", "T", "E", "D", "G", "H" ], "lines": [ "line A C", "line D G K", "line A T K", "line A E G F H", "line B D E T C", "line B A", "line D F" ], "circles": [], "semantics": [ "BC \\perp DF on D" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8047.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "D", "C", "A", "E" ], "lines": [ "line D C", "line D A E F", "line B E C", "line B F", "line B A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8049.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "E" ], "lines": [ "line A C", "line B E", "line B D C", "line A E D", "line A B", "line E C" ], "circles": [], "semantics": [ "m \\angle EBA = m \\angle 1", "m \\angle AEC = m \\angle 4", "m \\angle ACE = m \\angle 2", "m \\angle BEA = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8053.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "E", "B", "C" ], "lines": [ "line C A", "line O E A", "line O C", "line B O", "line B C", "line C E" ], "circles": [], "semantics": [ "OA \\perp CE on E", "m \\angle COB = m \\angle 1", "m \\angle OBC = m \\angle 3", "m \\angle EOC = m \\angle 2", "m \\angle CAE = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8059.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "H", "D", "F", "E", "G", "I" ], "lines": [ "line A B", "line A F E I H", "line C D H", "line F G D", "line C G E B", "line D I B", "line A C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8062.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "H", "D", "C", "F", "B", "G" ], "lines": [ "line D H C F", "line A G F", "line A B", "line E B G C", "line A H", "line E F", "line A E", "line A D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8063.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "M", "D", "C", "B", "E", "F" ], "lines": [ "line C B", "line E F B", "line M B", "line A B", "line M F A", "line D A", "line E M", "line D M C" ], "circles": [], "semantics": [ "m \\angle FME = m \\angle \\alpha", "m \\angle FBA = m \\angle \\beta" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8073.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "G", "C", "A", "B", "F", "E", "H", "I" ], "lines": [ "line A F C", "line F H D", "line G D", "line E F", "line B I H C", "line A E B G", "line B D", "line D C", "line E I D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8086.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "C", "A", "G", "D", "F", "H" ], "lines": [ "line A H G E", "line A F C", "line B C E", "line D G C", "line F G", "line D E", "line B F H D", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8091.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B F A", "line C A", "line E F D C", "line B C", "line D A", "line B E" ], "circles": [], "semantics": [ "EC \\perp DA on D", "EC \\perp BE on E", "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8094.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "F", "B", "C", "E" ], "lines": [ "line D B F", "line C B", "line A E B", "line E D", "line A C", "line E C F" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8096.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "A", "E", "B", "F", "G", "H" ], "lines": [ "line A F H C", "line D C", "line D G F E", "line E H B", "line A G B", "line D B", "line B C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8103.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "C", "D", "B", "P", "O" ], "lines": [ "line B O", "line A O", "line A C", "line E P O", "line B P D", "line O D", "line B E", "line O C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8130.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "P", "O", "D", "Q", "B", "C", "F", "G", "H" ], "lines": [ "line 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"line B M D N C", "line P E Q", "line A E D", "line A P B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8630.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "C", "E", "F", "O", "M", "G" ], "lines": [ "line D C", "line A M O C", "line B C", "line F C", "line B O G D", "line A B", "line E M G F", "line A E", "line A D" ], "circles": [], "semantics": [ "FC \\perp EF on F", "EF \\perp AE on E" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8638.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "A", "M", "F", "N", "E" ], "lines": [ "line B C", "line F E C", "line A E", "line D N C", "line D E B", "line A D", "line A F M B", "line M E N" ], "circles": [], "semantics": [ "FC \\perp DB on E", "AB \\perp MN on M" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8656.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "B", "C", "F", "D", "G", "H" ], "lines": [ "line B D A", "line E G F", "line D F", "line C F A", "line E H D", "line B H G C" ], "circles": [], "semantics": [ "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8659.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "G", "F", "A", "C", "D", "N", "E", "H", "I" ], "lines": [ "line B C", "line F I H C", "line H D", "line A E I D", "line F E", "line F G", "line A B", "line H N", "line G D N C" ], "circles": [], "semantics": [ "HN \\perp GC on N" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8662.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "A", "M", "C", "D", "E" ], "lines": [ "line A E C", "line B M C F", "line A D B", "line D E F", "line E M" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8664.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "A", "G", "E", "F", "P", "R", "Q" ], "lines": [ "line F G", "line A P C", "line D R E", "line B C E G", "line F E", "line D Q C", "line B P Q R F", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8676.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "M", "B", "N", "H", "E", "D", "C" ], "lines": [ "line M B", "line C N", "line C D B", "line D E", "line A N H E B", "line A C M", "line D H" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8677.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "E", "F", "C", "G" ], "lines": [ "line D C", "line A F", "line A G E", "line G D", "line B F E C", "line E D", "line A B", "line A D" ], "circles": [], "semantics": [ "AF \\perp BC on F", "AE \\perp GD on G" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8679.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "F", "B", "E", "G", "H" ], "lines": [ "line C F D", "line C B", "line A B", "line B F", "line A E C", "line E B", "line G B", "line C H" ], "circles": [], "semantics": [ "m \\angle CBG = 15" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8685.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "B", "G", "C", "D", "E", "H" ], "lines": [ "line B E A", "line F D", "line C H D A", "line E H F", "line E D", "line G E", "line B G C F" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8686.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "M", "H", "E", "A", "F", "D" ], "lines": [ "line C B", "line H F", "line E F D", "line D A", "line A M B", "line C F A", "line C M", "line E H A" ], "circles": [], "semantics": [ "AB \\perp CM on M" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8705.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "G", "C", "L", "H", "D", "J", "I", "F", "K", "B", "O" ], "lines": [ "line A I B J", "line A H O D E", "line L F K E", "line C B O F G", "line I H L G", "line C J D K", "line A C", "line H B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8715.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "O", "A", "C", "F", "E", "G", "H", "I", "J" ], "lines": [ "line A E B", "line F E", "line x lieson J O D B G", "line y lieson H C O I", "line D E", "line C F A", "line C D" ], "circles": [], "semantics": [ "AB \\perp line x on B" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8721.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line B D", "line A C G", "line E H D", "line F D", "line C E B", "line A F", "line F G H", "line A B" ], "circles": [], "semantics": [ "m \\angle CAB = m \\angle \\alpha" ] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8724.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "G", "E", "D", "F" ], "lines": [ "line C E B", "line F B", "line A G B", "line E F", "line C D A", "line F G", "line D F", "line A F" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8733.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "A", "D", "C", "E", "O", "G", "H" ], "lines": [ "line A F C", "line B D C", "line A G D", "line E H G F", "line B E O A", "line D F", "line O H D" ], "circles": [ "\\odot O lieson A F D E" ], "semantics": [] }, { "diagram": "PGDP/printed/image/PGDP10K_new_8735.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "P", "C", "D", "M", "E", "O", "B", "N", "F" ], "lines": [ "line D E P", "line O M", "line D N M", "line D B", "line A O N F B P", "line D F", "line C E B", "line A D C", "line A M", "line M B" ], "circles": [ "\\odot O lieson A D B M" ], "semantics": [ "AP \\perp DF on F" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_0.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "E" ], "lines": [ "line A B E", "line D B C", "line A C" ], "circles": [], "semantics": [ "AB = 4", "AC = \\sqrt{10}", "CB = 2", "m \\angle EBD = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_1.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D B", "line A B", "line C A", "line D A" ], "circles": [], "semantics": [ "AB \\perp CA on A", "CB \\perp DA on D", "AC = y", "CD = 3", "AB = z", "AD = x", "DB = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_2.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "T", "U", "R", "S" ], "lines": [ "line S R", "line U R", "line T U", "line T S" ], "circles": [], "semantics": [ "m \\angle URS = 6x-54", "m \\angle STU = 4x+6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_3.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C E A", "line D E B" ], "circles": [], "semantics": [ "m \\angle CED = m \\angle 17", "m \\angle AEB = m \\angle 18" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_4.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line B C", "line A C" ], "circles": [], "semantics": [ "BC \\perp AC on C", "m \\angle BAC = x", "m \\angle ABC = 31" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_5.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B", "X", "P" ], "lines": [ "line A X D", "line A B", "line C X B", "line C D" ], "circles": [ "\\odot P lieson C A B D" ], "semantics": [ "AB = CD", "m \\angle AXB = m \\angle 1", "m \\angle DXC = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_6.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line D A E", "line A B" ], "circles": [ "\\odot F lieson A B C" ], "semantics": [ "m \\angle EAB = 96" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_7.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "B", "D", "A" ], "lines": [ "line B D A", "line C D", "line C A", "line B C" ], "circles": [], "semantics": [ "CA \\perp BC on C", "BA \\perp CD on D", "BD = 8", "AD = 3", "CA = y", "DC = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_8.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line B C", "line A C" ], "circles": [], "semantics": [ "BC \\perp AC on C", "BA = 13", "AC = x", "BC = 11" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_9.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J" ], "lines": [ "line J H E F", "line A C D F", "line G H I A", "line G E D B", "line J I C B" ], "circles": [], "semantics": [ "m \\angle HGE = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_10.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Z", "W", "X", "Y", "A" ], "lines": [ "line W X", "line X Y", "line Z Y", "line W Z", "line W A Y", "line Z A X" ], "circles": [], "semantics": [ "m \\angle XWA = m \\angle 8", "m \\angle WXA = m \\angle 1", "m \\angle ZWA = m \\angle 7", "m \\angle YXA = m \\angle 2", "m \\angle WAX = m \\angle 11", "m \\angle WAZ = m \\angle 9", "m \\angle YAX = m \\angle 10", "m \\angle YAZ = m \\angle 12", "m \\angle WZA = m \\angle 6", "m \\angle XYA = m \\angle 3", "m \\angle YZA = m \\angle 5", "m \\angle ZYA = m \\angle 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_11.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line A B F", "line A C E", "line D C B G" ], "circles": [], "semantics": [ "m \\angle BCE = 100", "m \\angle FBG = 75", "m \\angle CAB = m \\angle 3", "m \\angle ABG = m \\angle 2", "m \\angle ACB = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_12.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line B C", "line D C", "line A D" ], "circles": [], "semantics": [ "AB = 15", "BC = 20", "m \\angle BCD = 30", "m \\angle CDA = 135" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_13.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line F A B", "line B C G", "line E D B" ], "circles": [], "semantics": [ "FB \\perp BG on B" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_14.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J" ], "lines": [ "line I C A E G", "line H B A D F" ], "circles": [ "\\odot J lieson B C D E" ], "semantics": [ "m \\angle CAB = m \\angle 5", "m \\widehat DC = 150", "m \\widehat BE = 110" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_15.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "T", "S", "R", "A", "B", "C", "D" ], "lines": [ "line A Q T D", "line B R S C", "line T S", "line Q R" ], "circles": [], "semantics": [ "QR \\parallel TS", "m \\angle RQA = m \\angle 1", "m \\angle RQT = m \\angle 2", "m \\angle STQ = m \\angle 3", "m \\angle QRS = m \\angle 6", "m \\angle QRB = m \\angle 5", "m \\angle STD = m \\angle 4", "m \\angle TSR = m \\angle 7", "m \\angle TSC = m \\angle 8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_16.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "R", "S", "Q" ], "lines": [ "line R Q P", "line P S", "line Q S" ], "circles": [ "\\odot Q lieson R S P" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_17.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D B", "line C B", "line C A", "line C D" ], "circles": [], "semantics": [ "AB \\perp CD on D", "CA = 17", "CB = 25", "CD = 15" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_18.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "R", "B" ], "lines": [ "line P B R", "line Q R", "line Q B", "line P Q" ], "circles": [], "semantics": [ "m \\angle BQP = m \\angle RQB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_19.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B" ], "lines": [ "line C B", "line C A" ], "circles": [ "\\odot C lieson A B" ], "semantics": [ "BC = 1", "m \\angle BCA = 90" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_20.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "Z", "T", "Y", "W", "A" ], "lines": [ "line Z Y T", "line X W T" ], "circles": [ "\\odot A lieson Z X W Y" ], "semantics": [ "TY = 6", "TW = 7", "ZY = x", "XW = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_21.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Y", "X", "Z", "W" ], "lines": [ "line Y W", "line X W", "line X Y", "line X Z", "line Z W" ], "circles": [], "semantics": [ "YW = ZW = 10", "XZ = XY = XW", "m \\angle XZW = m \\angle 4 = m \\angle XWZ = m \\angle 3 = m \\angle WYX = m \\angle 1 = m \\angle YWX = m \\angle 2", "m \\angle WXZ = m \\angle 5", "m \\angle WXY = m \\angle 6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_22.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line B D", "line A B", "line C D" ], "circles": [], "semantics": [ "BD = m+7", "AC = 3m-12", "m \\angle BDC = 3x", "m \\angle ACD = 8x+15" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_23.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Y", "Z", "X", "A", "B" ], "lines": [ "line Y Z B", "line Y X A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_24.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "N", "P", "Q", "R", "A", "B" ], "lines": [ "line P A R", "line N A Q" ], "circles": [ "\\odot B lieson N P Q R" ], "semantics": [ "m \\angle NAP = 51", "m \\widehat NP = 74" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_25.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "L", "J", "C", "K", "B" ], "lines": [ "line A B", "line C B", "line A C", "line L J", "line J K", "line L K" ], "circles": [], "semantics": [ "CA = 6", "LJ = 10\\frac{2}{3}", "JK = BC = 8", "m \\angle LJK = m \\angle BCA = 110" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_26.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line C D", "line A D", "line B A", "line B D" ], "circles": [], "semantics": [ "AD \\perp BA on A", "DA = x", "CD = BA = 20", "BD = 29" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_27.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line E C", "line E A D", "line C D", "line C A B", "line B D" ], "circles": [], "semantics": [ "EC \\perp CD on C", "CD \\perp BD on D", "EC = BD = CD", "m \\angle ABD = y", "m \\angle ECA = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_28.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B C E", "line A B", "line A D", "line D E", "line A C", "line A F E", "line D F" ], "circles": [], "semantics": [ "AE \\perp DF on F", "BE \\perp AC on C", "BE = 21", "DF = 4", "AC = 6", "AE = 18" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_29.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D A", "line C A", "line C B D" ], "circles": [ "\\odot B lieson C A D" ], "semantics": [ "DA \\perp CA on A", "AC = 21", "DA = 13" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_30.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "D", "F", "B", "C", "E" ], "lines": [ "line A B C", "line D C", "line B E D", "line F A" ], "circles": [], "semantics": [ "AC \\perp DC on C" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_31.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "J", "P", "Q", "K", "M", "L", "N", "A" ], "lines": [ "line M K Q P", "line M L N", "line J Q N" ], "circles": [ "\\odot A lieson J P N L K" ], "semantics": [ "m \\angle PQN = 79", "m \\widehat JP = 86", "m \\widehat JK = 48" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_32.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "S", "R" ], "lines": [ "line P S", "line R S", "line Q R", "line Q P" ], "circles": [], "semantics": [ "m \\angle PQR = 2x-16", "m \\angle RSP = x+10", "m \\angle QPS = x", "m \\angle SRQ = 2x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_33.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "P", "Q", "S" ], "lines": [ "line R Q", "line P S Q", "line R P", "line R S" ], "circles": [], "semantics": [ "m \\angle SPR = m \\angle RQS" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_34.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line C A", "line C B" ], "circles": [], "semantics": [ "BA \\perp CB on B", "CB = 0.34", "BA = 0.15", "m \\angle BAC = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_35.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line m lieson H B F", "line l lieson G A E", "line D A B C" ], "circles": [], "semantics": [ "m \\angle GAD = 9x-4", "m \\angle FBC = 140" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_36.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D E B", "line A B", "line C E A", "line D C", "line D A", "line C B" ], "circles": [], "semantics": [ "EC = AE" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_37.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "Y", "X", "Z" ], "lines": [ "line A Z C", "line A X B", "line C Y B", "line Z X", "line X Y", "line Z Y" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_38.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "G", "J", "K", "H" ], "lines": [ "line J H", "line G H", "line J K G", "line F J", "line F G", "line F K H" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_39.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line B D", "line A C D", "line B A", "line B C", "line G H", "line E F H", "line G F", "line G E" ], "circles": [], "semantics": [ "BA = 2x+1", "BD = 40", "GH = 25", "GE = x+4", "EF = FH", "m \\angle BDC = m \\angle GHF" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_40.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "R", "B" ], "lines": [ "line A R", "line B R" ], "circles": [ "\\odot R lieson A B" ], "semantics": [ "BR = 5", "m \\angle ARB = 105" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_41.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A", "line B A" ], "circles": [ "\\odot C lieson B A" ], "semantics": [ "m \\widehat BA = 158", "m major \\widehat BA = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_42.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "E", "F", "G", "H", "I" ], "lines": [ "line G A C E F", "line I D C B H" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_43.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D B", "line D A", "line A C", "line B C" ], "circles": [], "semantics": [ "m \\angle BDA = m \\angle DBC = m \\angle DAC = m \\angle ACB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_44.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "C", "P" ], "lines": [ "line A B", "line C B", "line D C", "line A D" ], "circles": [ "\\odot P lieson A B C D" ], "semantics": [ "m \\angle BAD = 2y", "m \\angle CDA = 3y", "m \\angle ABC = 3x", "m \\angle BCD = 5x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_45.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "F", "D" ], "lines": [ "line E F", "line E D", "line F D" ], "circles": [], "semantics": [ "FE = 31", "ED = 20", "m \\angle EDF = 84" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_46.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C" ], "lines": [ "line D C", "line B C", "line A B", "line A D" ], "circles": [], "semantics": [ "AB \\parallel DC", "m \\angle DAB = x", "m \\angle ADC = 65" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_47.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B", "E" ], "lines": [ "line D C", "line A E C", "line A B", "line D E B", "line D A", "line C B" ], "circles": [], "semantics": [ "DA = CB", "m \\angle EAD = m \\angle EBC = m \\angle EAB = m \\angle ABE" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_48.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D" ], "lines": [ "line A B", "line C B" ], "circles": [ "\\odot D lieson A C B" ], "semantics": [ "m \\angle ABC = 24" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_49.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "T", "U", "V" ], "lines": [ "line V U", "line T U", "line T V" ], "circles": [], "semantics": [ "VU = TV", "m \\angle UTV = m \\angle VUT = 42" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_50.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "S", "R", "Q", "U", "T", "A", "B", "C" ], "lines": [ "line R T Q B", "line R U S A" ], "circles": [ "\\odot C lieson U S Q T" ], "semantics": [ "m \\widehat QS = 103", "m \\widehat TU = 43" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_51.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line E C B", "line E A", "line E D", "line A B", "line D B", "line D C A" ], "circles": [], "semantics": [ "ED = 13", "EC = 12", "BC = 8", "DB = AB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_52.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "E" ], "lines": [ "line C D B E A" ], "circles": [ "\\odot C lieson D", "\\odot B lieson D E", "\\odot A lieson E" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_53.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line C B A", "line A F E D" ], "circles": [ "\\odot G lieson B E F" ], "semantics": [ "m \\angle BAF = x", "m \\widehat FB = 68", "m \\widehat EB = 160" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_54.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "W", "Z", "U", "Y" ], "lines": [ "line W Z", "line W Y", "line Z U Y", "line W U" ], "circles": [], "semantics": [ "ZY \\perp WU on U", "ZU = x+6", "YU = 32", "ZW = 3x-6", "WY = 40", "m \\angle ZWU = m \\angle WYU" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_55.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "D", "E" ], "lines": [ "line D F", "line D E", "line F E" ], "circles": [], "semantics": [ "FD = 3b", "EF = 3", "DE = 3c" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_56.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C D A", "line E A", "line B E", "line B D", "line B C" ], "circles": [], "semantics": [ "CA \\perp BD on D", "EB = 12", "CA = 35", "DB = 13" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_57.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E" ], "lines": [ "line D E B", "line A E C", "line D C", "line A B", "line A D", "line B C" ], "circles": [ "\\odot E lieson D A B C" ], "semantics": [ "m \\angle EAB = m \\angle 1", "m \\angle EAD = m \\angle 11", "m \\angle EBA = m \\angle 3", "m \\angle DEA = m \\angle 12", "m \\angle BEA = m \\angle 2", "m \\angle EDA = m \\angle 10", "m \\angle EBC = m \\angle 5", "m \\angle DEC = m \\angle 8", "m \\angle BEC = m \\angle 4", "m \\angle EDC = m \\angle 7", "m \\angle ECD = m \\angle 9", "m \\angle ECB = m \\angle 6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_58.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "E", "F", "G" ], "lines": [ "line D F", "line D E", "line G F", "line E F", "line D G" ], "circles": [], "semantics": [ "DE \\parallel GF", "m \\angle DEF = m \\angle FGD" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_59.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "W", "Z", "Y", "X", "A", "B", "C", "D" ], "lines": [ "line D W X Y B", "line C Z X A" ], "circles": [], "semantics": [ "DB \\perp CA on X", "WX = XY" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_60.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A C", "line C F D", "line B H E D", "line A B", "line A H", "line G F", "line G E" ], "circles": [], "semantics": [ "BD \\perp AB on B", "CD \\perp BD on D", "BH = 50", "CA = 250", "BA = 120", "DE = 100", "FD = GF = GE" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_61.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D A", "line A B", "line D B", "line C B" ], "circles": [], "semantics": [ "m \\angle DAB = 66", "m \\angle DCB = 24", "m \\angle ADB = m \\angle 3", "m \\angle DBA = m \\angle 1", "m \\angle CDB = m \\angle 4", "m \\angle DBC = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_62.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "J", "K", "L" ], "lines": [ "line J K", "line J L", "line K L" ], "circles": [], "semantics": [ "JL = KL", "m \\angle JLK = 82" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_63.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D C", "line B C", "line A B", "line A D" ], "circles": [], "semantics": [ "AB \\parallel DC", "AD = BC", "m \\angle BCD = 101" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_64.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C A", "line B C", "line B A" ], "circles": [], "semantics": [ "CB = 2x+11", "AC = 6x-9", "m \\angle BCA = m \\angle ABC = m \\angle BAC" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_65.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "W", "Z", "Y", "U" ], "lines": [ "line W U Y", "line Y Z", "line X U Z", "line X Y", "line W Z", "line W X" ], "circles": [], "semantics": [ "WY \\perp XZ on U", "XU = ZU = YU = 12", "WU = 20" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_66.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line B C", "line A C", "line F E", "line E D", "line F D" ], "circles": [], "semantics": [ "FE = AB", "m \\angle EDF = m \\angle BCA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_67.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A C", "line D C", "line D B" ], "circles": [ "\\odot A lieson D C B" ], "semantics": [ "BD = 5", "m \\angle DCA = 30" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_68.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C B", "line B A", "line C A" ], "circles": [], "semantics": [ "m \\angle BCA = m \\angle BAC = m \\angle CBA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_69.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "S", "Q" ], "lines": [ "line Q R", "line S R", "line S Q" ], "circles": [], "semantics": [ "QR = 21", "QS = 33.2", "RS = 53", "m \\angle SRQ = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_70.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line F G H E", "line A G C", "line B H D" ], "circles": [], "semantics": [ "AC \\parallel BD", "m \\angle FGC = 151", "m \\angle EHB = 2x+1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_71.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "S", "R", "P" ], "lines": [ "line P R", "line Q R S", "line P Q", "line P S" ], "circles": [ "\\odot P lieson Q S" ], "semantics": [ "PR \\perp QS on R", "PR = 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_72.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line D A", "line C D", "line C B" ], "circles": [], "semantics": [ "BA \\perp CB on B", "BA \\perp DA on A", "CB = 10", "BA = 15", "AD = 14" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_73.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C D", "line D A E", "line C B E", "line B A" ], "circles": [], "semantics": [ "CD \\parallel BA", "CB = \\frac{1}{5}x+3", "DA = 2y+1", "EB = 4x-35", "EA = DA = 5y-8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_74.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "E", "H", "G" ], "lines": [ "line E H", "line G H", "line F G", "line F E" ], "circles": [], "semantics": [ "HG = 2x-3", "m \\angle HEF = 7y+9" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_75.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line B C", "line A C" ], "circles": [], "semantics": [ "AB \\perp BC on B", "AB = x", "BC = 4", "CA = 16" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_76.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "E", "F" ], "lines": [ "line D B A", "line F B E" ], "circles": [ "\\odot C lieson F D E A" ], "semantics": [ "DB = 5", "FB = 6", "EB = 8", "AB = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_77.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "Z", "Y" ], "lines": [ "line X Z", "line Z Y", "line X Y" ], "circles": [], "semantics": [ "XZ \\perp ZY on Z", "XZ = y", "YX = 4", "m \\angle ZYX = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_78.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C B", "line C A", "line B A D" ], "circles": [], "semantics": [ "m \\angle BCA = 38", "m \\angle CAD = 10x+9", "m \\angle CBA = 7x+1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_79.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "G", "H" ], "lines": [ "line H G", "line E G", "line E H" ], "circles": [], "semantics": [ "HG \\perp EH on H", "EH = HG", "m \\angle HGE = 3x+6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_80.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "S", "U", "T", "A" ], "lines": [ "line U A S", "line R A T" ], "circles": [], "semantics": [ "RA = 3(a+b)", "TA = 3c", "UA = 3a", "SA = 3(b+c)" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_81.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B", "E" ], "lines": [ "line C E A", "line D E B", "line C B", "line D C", "line D A", "line A B" ], "circles": [], "semantics": [ "CB \\perp DC on C", "DC \\perp DA on D", "CA \\perp DB on E", "DA \\perp AB on A", "CB \\perp AB on B", "CE = DE = EA = EB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_82.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "M" ], "lines": [ "line P Q", "line P M", "line Q M" ], "circles": [], "semantics": [ "PQ = 11", "QM = p", "PM = 10", "m \\angle QPM = 38" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_83.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D A", "line B D", "line B C", "line B A" ], "circles": [], "semantics": [ "BC \\perp BA on B", "CA \\perp BD on D", "CB = y", "CD = z", "DA = 10", "BA = 12", "BD = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_84.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "I", "F", "E", "A", "B", "C" ], "lines": [ "line C G F", "line B E F", "line F I A" ], "circles": [], "semantics": [ "m \\angle GFE = 9x-2", "m \\angle EFI = 4x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_85.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C B", "line C D", "line D A", "line B A", "line C A" ], "circles": [], "semantics": [ "BA \\perp CA on A", "CB = 10", "m \\angle CBA = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_86.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "T", "R", "S" ], "lines": [ "line S R", "line T R", "line T S" ], "circles": [], "semantics": [ "SR \\perp TS on S", "RT = 23", "TS = 11" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_87.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "T", "S", "F", "B", "C", "D", "A", "U", "V", "E" ], "lines": [ "line T A D C", "line S B F C", "line S V U T", "line U A", "line U E F", "line D F", "line V E D", "line V B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_88.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line 6 lieson E A C", "line a lieson B A D" ], "circles": [], "semantics": [ "m \\angle CAB = m \\angle 1", "m \\angle EAB = m \\angle 2", "m \\angle EAD = m \\angle 3", "m \\angle CAD = m \\angle 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_89.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line C A", "line B C" ], "circles": [], "semantics": [ "CA \\perp BC on C", "AC = x", "BA = 10", "m \\angle ABC = m \\angle BAC = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_90.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B C", "line A B" ], "circles": [], "semantics": [ "m \\angle ACB = 38", "m \\angle CAB = 10x+22", "m \\angle CBA = 7x+1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_91.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "J", "P", "R", "Q", "K", "L" ], "lines": [ "line K L", "line J K", "line J L", "line P Q", "line R Q", "line P R" ], "circles": [], "semantics": [ "KJ = 12", "PQ = 15" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_92.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "K", "J", "L", "M", "N", "P" ], "lines": [ "line P N", "line J P L", "line K P M" ], "circles": [ "\\odot P lieson J K L M N" ], "semantics": [ "PN \\perp JL on P" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_93.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E" ], "lines": [ "line D C", "line B C", "line A B", "line A D", "line D E B", "line A E C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_94.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "H", "G", "J", "A" ], "lines": [ "line G H", "line J A H", "line J G" ], "circles": [ "\\odot J lieson A G" ], "semantics": [ "GH = 12", "JG = 5", "HJ = 14" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_95.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line B C", "line A C" ], "circles": [], "semantics": [ "AB = 2.8", "CA = 4", "BC = 3.1", "m \\angle ABC = 85", "m \\angle BAC = 51" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_96.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D C", "line A D", "line A B", "line B C E" ], "circles": [], "semantics": [ "m \\angle CDA = 70", "m \\angle DAB = 72", "m \\angle ABC = 111", "m \\angle DCE = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_97.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line B C", "line B D", "line A D", "line B A", "line C D" ], "circles": [], "semantics": [ "BD \\perp CD on D", "AD \\perp BA on A", "m \\angle DBA = 58", "m \\angle BCD = 64", "m \\angle CBD = m \\angle 1", "m \\angle BDA = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_98.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "T", "X", "R", "B", "C" ], "lines": [ "line C T X", "line B R X", "line T A", "line A R", "line A X" ], "circles": [], "semantics": [ "m \\angle TXA = m \\angle RXA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_99.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line B A D", "line C A", "line C D" ], "circles": [], "semantics": [ "CB = 15", "BA = x", "DA = 7", "DC = 14", "m \\angle BCA = m \\angle ACD" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_100.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C D", "line A B" ], "circles": [ "\\odot E lieson A D C" ], "semantics": [ "AB = 8", "BC = x", "CD = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_101.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line C D", "line B C", "line D E", "line E F", "line F G", "line G H", "line A H", "line B A" ], "circles": [], "semantics": [ "BC = CD = DE = EF = FG = GH = 3", "AB = 9" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_102.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "E", "A" ], "lines": [ "line B C D", "line C A", "line A E" ], "circles": [ "\\odot A lieson B D E" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_103.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "J", "K", "L" ], "lines": [ "line J M K", "line L K", "line J L", "line M L" ], "circles": [], "semantics": [ "JK \\perp ML on M", "LK \\perp JL on L", "JM = 8", "KM = 16" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_104.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "G", "B", "H", "D", "E", "F", "C", "I" ], "lines": [ "line A D E", "line B C F H", "line G F E I", "line G H", "line G B A", "line G C D" ], "circles": [], "semantics": [ "GH \\perp GD on G", "AE \\perp GD on D", "m \\angle FGH = m \\angle DEF = 50" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_105.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B D", "line C D", "line C B" ], "circles": [], "semantics": [ "m \\angle ABC = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_106.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line B A D F", "line C A G I", "line E D G H" ], "circles": [], "semantics": [ "m \\angle BAC = m \\angle 1", "m \\angle BAG = m \\angle 2", "m \\angle DAC = m \\angle 3", "m \\angle DAG = m \\angle 4", "m \\angle AGH = m \\angle 10", "m \\angle AGD = m \\angle 9", "m \\angle ADG = m \\angle 6", "m \\angle IGH = m \\angle 12", "m \\angle ADE = m \\angle 5", "m \\angle IGD = m \\angle 11", "m \\angle FDE = m \\angle 7", "m \\angle FDG = m \\angle 8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_107.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line B C", "line C", "line E D", "line F E", "line F", "line F C", "line B F", "line A F", "line F D" ], "circles": [], "semantics": [ "ED \\perp FD on D", "DF = 5.6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_108.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "C", "Q" ], "lines": [], "circles": [ "\\odot Q lieson A B C D" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_109.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "E", "B", "F", "D", "C", "R" ], "lines": [ "line E F D", "line R F", "line C R", "line A C B" ], "circles": [ "\\odot R lieson A B D E" ], "semantics": [ "CR \\perp AB on C", "ED \\perp RF on F" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_110.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line A C D E", "line m lieson F D G H", "line n lieson B C G I" ], "circles": [], "semantics": [ "m \\angle DCG = m \\angle 1", "m \\angle DGC = m \\angle 3", "m \\angle CDG = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_111.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line A C", "line A B" ], "circles": [], "semantics": [ "AB = x", "CB = 17", "m \\angle ACB = 39", "m \\angle CBA = 96" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_112.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "D", "P", "C", "Q", "S", "R", "B" ], "lines": [ "line D C", "line B C", "line A D", "line A B", "line R S", "line Q S", "line R P", "line P Q" ], "circles": [], "semantics": [ "m \\angle QSR = 98", "m \\angle SRP = 3y-13", "m \\angle DCB = 83", "m \\angle BAD = 82", "m \\angle RPQ = 97", "m \\angle CDA = x+34" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_113.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "N", "L", "P", "A" ], "lines": [ "line N P", "line L P", "line L M N", "line M P A" ], "circles": [], "semantics": [ "LN \\perp MA on M", "LM = NM = 10", "PL = 2x-4", "PN = x+5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_114.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Y", "X", "Z" ], "lines": [ "line Y Z", "line X Z", "line X Y" ], "circles": [], "semantics": [ "YZ \\perp XY on Y", "m \\angle XZY = \\frac{a}{2}", "m \\angle YXZ = 2a" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_115.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line D A", "line D C", "line A B C", "line D B", "line F G H", "line E F", "line E G", "line E H" ], "circles": [], "semantics": [ "AD = 2x", "EG = x", "FE = 5", "BD = 10", "AB = BC", "m \\angle DAB = m \\angle GFE" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_116.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "E", "F", "D" ], "lines": [ "line E F", "line B D F", "line A B", "line A C E", "line C D" ], "circles": [], "semantics": [ "EF \\perp AE on E", "m \\angle EFD = 80", "m \\angle DBA = m \\angle FDC = 100", "m \\angle BAC = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_117.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "M", "N", "L", "P", "B" ], "lines": [ "line A B", "line D C", "line M L", "line N P", "line D A", "line C B", "line N M", "line P L" ], "circles": [], "semantics": [ "NM = x+6", "AB = 14", "CB = 10", "ML = x+9", "m \\angle BAD = m \\angle MLP" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_118.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line B F", "line G F E", "line C G", "line A H G", "line D H" ], "circles": [], "semantics": [ "DH \\parallel CG \\parallel BF", "m \\angle GHD = 7x+9", "m \\angle CGF = 11x-1", "m \\angle BFG = 2y+5", "m \\angle DHA = z", "m \\angle CGH = 7y-4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_119.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B D", "line D E", "line A E", "line B A", "line B C E", "line A C D" ], "circles": [], "semantics": [ "AE = DE = BD = BA", "m \\angle EAC = 32", "m \\angle DBC = m \\angle 1", "m \\angle BDC = m \\angle 2", "m \\angle ECD = m \\angle 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_120.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "K", "R", "M", "N", "J", "T" ], "lines": [ "line K R", "line M N", "line J T", "line K M J", "line R N T" ], "circles": [], "semantics": [ "KR \\parallel JT", "NM = 52.5", "TJ = 32.5", "KM = JM" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_121.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "W", "V", "X", "Z", "A", "B", "C", "D", "E" ], "lines": [ "line B Z A", "line W A", "line C X W V D", "line W Z E" ], "circles": [], "semantics": [ "m \\angle XWZ = m \\angle 1", "m \\angle AWV = m \\angle 2", "m \\angle AWZ = m \\angle 3", "m \\angle AZW = m \\angle 5", "m \\angle ZAW = m \\angle 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_122.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line C B D", "line C A", "line A B" ], "circles": [], "semantics": [ "m \\angle BCA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_123.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "S", "T" ], "lines": [ "line R T", "line S T", "line R S" ], "circles": [], "semantics": [ "ST \\perp RS on S", "SR = 25", "RT = 30" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_124.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B D A", "line C A", "line C B", "line C D" ], "circles": [], "semantics": [ "BA \\perp CD on D", "CA = 8.5", "CB = 5", "CD = 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_125.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line A B", "line B C", "line D C" ], "circles": [], "semantics": [ "m \\angle ABC = 108", "m \\angle BCD = 3x", "m \\angle ADC = 67", "m \\angle DAB = 4x+10" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_126.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C A D", "line B A E" ], "circles": [ "\\odot F lieson B D E C" ], "semantics": [ "BA = 2", "CA = 4", "DA = 5", "EA = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_127.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "R", "P", "N", "A" ], "lines": [ "line M N P", "line M R" ], "circles": [ "\\odot A lieson N P R" ], "semantics": [ "m \\angle NMR = x", "m \\widehat NP = 108", "m \\widehat NR = 62" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_128.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "Y", "Z", "W" ], "lines": [ "line W Z", "line Y Z", "line X Y", "line X W" ], "circles": [], "semantics": [ "m \\angle WXY = x", "m \\angle XWZ = 3x", "m \\angle ZYX = 2x", "m \\angle YZW = 4x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_129.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A F", "line F E", "line D E", "line C D", "line B C", "line B A" ], "circles": [], "semantics": [ "BC = CD = BA = DE = AF = FE", "m \\angle DCB = m \\angle CBA = m \\angle EDC = m \\angle FAB = m \\angle FED = m \\angle AFE" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_130.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A D", "line C B", "line C D" ], "circles": [ "\\odot A lieson B C D" ], "semantics": [ "BC = 12", "m \\angle CDA = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_131.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "C", "A", "B", "D", "F", "G", "H", "I" ], "lines": [ "line A G D F", "line B G C E" ], "circles": [ "\\odot H lieson C D B A", "\\odot I lieson C E F D" ], "semantics": [ "m \\angle AGC = m \\angle 2", "m \\angle AGB = m \\angle 3", "m \\angle DGC = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_132.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D E", "line C E", "line C B", "line E B" ], "circles": [ "\\odot A lieson D E B C" ], "semantics": [ "m \\angle DEC = a", "m \\angle CBE = c", "m \\angle CEB = b", "m \\widehat ED = 100", "m \\widehat CD = 60", "m \\widehat CB = 84", "m \\widehat EB = d" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_133.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "P", "T", "S" ], "lines": [ "line C P B", "line A T B", "line A S P", "line C S T", "line A C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_134.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "L" ], "lines": [ "line A B", "line A D" ], "circles": [ "\\odot L lieson B D" ], "semantics": [ "BA = x", "AD = 25" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_135.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "E", "A", "C", "B", "F" ], "lines": [ "line A B C", "line E B D" ], "circles": [ "\\odot F lieson A D C E" ], "semantics": [ "AB = 5", "EB = x", "DB = 10", "CB = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_136.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line D C A F", "line B F", "line B C E" ], "circles": [ "\\odot A lieson B F E D" ], "semantics": [ "DC = y", "FB = 12", "EC = 5", "CF = x", "l \\widehat DB = l \\widehat DE" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_137.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "E", "F" ], "lines": [ "line B F D", "line A F E" ], "circles": [ "\\odot C lieson B A D E" ], "semantics": [ "AF = 5", "DF = 8", "BF = 6", "EF = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_138.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D C A", "line E C B", "line B A", "line D B", "line D E", "line E A" ], "circles": [], "semantics": [ "EC = 4", "DC = 7", "CA = 11" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_139.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "B", "A", "E", "D", "C" ], "lines": [ "line A B", "line A F", "line F E", "line E D", "line C D", "line B C" ], "circles": [], "semantics": [ "m \\angle CDE = x-3", "m \\angle CBA = x-8", "m \\angle FED = x+6", "m \\angle BCD = x+7", "m \\angle FAB = x+2", "m \\angle AFE = x-4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_140.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line B F", "line E F G", "line C D E", "line A B D" ], "circles": [], "semantics": [ "m \\angle CDB = 2x", "m \\angle FBA = 3x", "m \\angle FED = x", "m \\angle BFG = 4x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_141.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "E" ], "lines": [ "line A E C", "line D C", "line B E D", "line B C", "line A B" ], "circles": [], "semantics": [ "BC \\perp AB on B", "DC \\perp BC on C" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_142.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C" ], "lines": [ "line B C", "line D C", "line A D", "line A B", "line A C" ], "circles": [], "semantics": [ "AB \\parallel DC", "DC = AB", "m \\angle BAC = m \\angle 1", "m \\angle DCA = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_143.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K" ], "lines": [ "line C J D", "line B I E", "line A G F", "line K J I G H" ], "circles": [], "semantics": [ "AF \\parallel BE \\parallel CD", "m \\angle IJD = 2y+8", "m \\angle KJD = 142", "m \\angle JIE = 4x+6", "m \\angle HGA = z" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_144.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line C B", "line A B" ], "circles": [], "semantics": [ "CB \\perp AB on B", "CB = 4", "BA = 8", "m \\angle ACB = x", "m \\angle CAB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_145.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C A", "line A D", "line C B D", "line A B" ], "circles": [], "semantics": [ "CD \\perp AB on B", "CA = AD = 30", "BA = x", "m \\angle BCA = 42" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_146.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "C", "A", "B", "D", "F", "G", "H", "I", "J", "K" ], "lines": [ "line F C B I", "line E D B J", "line A B K", "line H A D C", "line G E C", "line E A" ], "circles": [], "semantics": [ "m \\angle DEC = m \\angle 4", "m \\angle DEA = m \\angle 3", "m \\angle DCE = m \\angle 5", "m \\angle EDA = m \\angle 9", "m \\angle DAE = m \\angle 1", "m \\angle BCD = m \\angle 6", "m \\angle BAD = m \\angle 2", "m \\angle CBD = m \\angle 8", "m \\angle DBA = m \\angle 7" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_147.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A D", "line D C", "line D E", "line B E C", "line A B" ], "circles": [], "semantics": [ "DE \\perp BC on E", "DC = 4", "AD = 10", "DE = 5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_148.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line C D", "line B C", "line B A" ], "circles": [], "semantics": [ "CB = 2x+9", "AD = x+11", "m \\angle CBA = 106", "m \\angle CDA = 3y+19" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_149.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "F" ], "lines": [ "line A C", "line C D", "line B D", "line A B", "line A F D", "line B F" ], "circles": [], "semantics": [ "AC \\perp AB on A", "CD \\perp BD on D", "m \\angle FDB = 64", "m \\angle FAC = m \\angle 4", "m \\angle FAB = m \\angle 1", "m \\angle FBA = m \\angle 2", "m \\angle FBD = m \\angle 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_150.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C B", "line B A", "line D A", "line C D" ], "circles": [], "semantics": [ "m \\angle CBA = 96", "m \\angle BCD = 106", "m \\angle BAD = 88", "m \\angle ADC = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_151.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C E", "line E A", "line D A", "line C D", "line C B A", "line D B E" ], "circles": [], "semantics": [ "CB = 20", "DB = 30" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_152.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A B C D", "line D E F G" ], "circles": [ "\\odot H lieson B C E F" ], "semantics": [ "m \\angle EDC = x", "m \\widehat BC = 100", "m \\widehat BF = 120", "m \\widehat FE = 90" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_153.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line B C", "line A C", "line E F", "line D E", "line D F" ], "circles": [], "semantics": [ "DF = 8", "AC = 6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_154.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B A C", "line B E", "line E D", "line C D" ], "circles": [ "\\odot A lieson B C" ], "semantics": [ "BE = ED = 5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_155.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "A0", "A1" ], "lines": [ "line B A C" ], "circles": [ "\\odot A1 lieson B C" ], "semantics": [ "CB = 4", "\\Phi A1 = 6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_156.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line D A", "line C D", "line C B" ], "circles": [], "semantics": [ "DC = 15", "CB = x+5y", "BA = 3x+3y", "AD = 2x+y" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_157.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "O", "M", "N" ], "lines": [ "line M O", "line O N", "line M N" ], "circles": [], "semantics": [ "m \\angle ONM = 75" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_158.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C A", "line B A", "line B C" ], "circles": [], "semantics": [ "CA = 3.5", "BC = BA", "m \\angle BAC = 48" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_159.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O" ], "lines": [ "line k lieson G O L M K", "line m lieson E L N I", "line F A L C J", "line B L D H" ], "circles": [ "\\odot L lieson A B M C N D O" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_160.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "Q", "T", "P", "S", "A", "B", "C", "D" ], "lines": [ "line B P T S D", "line A R T", "line C Q T" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_161.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "F", "C", "D", "G" ], "lines": [ "line B A", "line B G C", "line A D C F", "line E F", "line D G E" ], "circles": [], "semantics": [ "EF \\parallel BC", "GC = EF" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_162.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "G", "F", "H", "J", "L" ], "lines": [ "line E J L F", "line G J H" ], "circles": [ "\\odot L lieson G F H E" ], "semantics": [ "EF \\perp GH on J" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_163.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E" ], "lines": [ "line B A", "line B C", "line D C", "line A D" ], "circles": [ "\\odot E lieson B C D A" ], "semantics": [ "m \\angle CDA = 23x+12", "m \\angle CBA = 21x-8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_164.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "F", "P", "E", "Q" ], "lines": [ "line D P E", "line F E", "line Q P", "line D Q F" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_165.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C E B", "line C D A" ], "circles": [ "\\odot F lieson D A B E" ], "semantics": [ "AD = BE = 5+x", "CD = x", "CE = 5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_166.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line F D E", "line B E", "line A C B", "line A F", "line C D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_167.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line E C B", "line F A B", "line A D", "line D C", "line D G B" ], "circles": [ "\\odot D lieson A G C" ], "semantics": [ "FB \\perp AD on A", "EB \\perp DC on C" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_168.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line A C", "line B D", "line B A", "line D C" ], "circles": [], "semantics": [ "m \\angle CBD = 28", "m \\angle CBA = 81", "m \\angle BCA = m \\angle 2", "m \\angle BCD = m \\angle 3", "m \\angle CAB = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_169.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "A", "B", "C", "D" ], "lines": [ "line D A", "line A B", "line D C", "line C B", "line D P B" ], "circles": [ "\\odot P lieson D C B A" ], "semantics": [ "DA \\perp AB on A", "DA = 5", "AB = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_170.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D B A", "line C B" ], "circles": [ "\\odot B lieson D C A" ], "semantics": [ "AD = 36", "m \\widehat CD = 30" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_171.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "S", "R", "U", "T", "V", "A" ], "lines": [ "line S V U", "line R V T" ], "circles": [ "\\odot A lieson R S T U" ], "semantics": [ "SV = x", "UV = 8", "RV = TV = 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_172.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line D C B" ], "circles": [ "\\odot E lieson C B" ], "semantics": [ "m \\angle ABC = x", "m \\widehat CB = 129" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_173.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "F", "B", "E", "G", "H", "I" ], "lines": [ "line E A B C G", "line B F H", "line B D I" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_174.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "N", "M", "O" ], "lines": [ "line N M", "line N O", "line M O" ], "circles": [], "semantics": [ "NM \\perp MO on M", "MN = 5", "OM = 12", "NO = 13", "m \\angle MNO = 67" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_175.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "J", "L", "A", "B", "C" ], "lines": [ "line M B L", "line C J B A", "line J L" ], "circles": [], "semantics": [ "ML \\perp CA on B", "MB = 6", "JL = 8.5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_176.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "M", "F", "K", "D", "H" ], "lines": [ "line D F", "line G D", "line G F", "line H K", "line M K", "line M H" ], "circles": [], "semantics": [ "MH = 15", "DF = 30", "HK = 18", "GF = 27.5", "m \\angle DGF = 70", "m \\angle FDG = 59" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_177.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "S", "R" ], "lines": [ "line S Q", "line Q R", "line S R", "line P S", "line P Q" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_178.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "W", "R", "T", "Z", "S", "V", "A" ], "lines": [ "line V Z", "line R A Z", "line Q R S", "line S T", "line W A T", "line Q W V" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_179.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line E D", "line E A B", "line E C", "line D A C", "line D B", "line B C" ], "circles": [], "semantics": [ "DB = BC", "m \\angle ABD = 46", "m \\angle DEA = 34", "m \\angle EDA = m \\angle 9", "m \\angle ADB = m \\angle 10", "m \\angle EAD = m \\angle 1", "m \\angle BAD = m \\angle 2", "m \\angle BAC = m \\angle 4", "m \\angle AEC = m \\angle 6", "m \\angle EAC = m \\angle 3", "m \\angle ABC = m \\angle 5", "m \\angle ACB = m \\angle 8", "m \\angle ECA = m \\angle 7" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_180.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "L", "T", "P", "S", "N" ], "lines": [ "line T P", "line P S", "line L N", "line T S", "line M N", "line M L" ], "circles": [], "semantics": [ "MN \\perp ML on M", "PS \\perp TS on S", "ML = 8", "PS = x+2", "MN = 10", "TS = x-1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_181.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line D C B", "line A C", "line E A", "line E D" ], "circles": [], "semantics": [ "AB \\perp DB on B", "AE = 40", "AB = 38", "CB = 28" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_182.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C", "E", "F", "G" ], "lines": [ "line A C F", "line E B A" ], "circles": [ "\\odot G lieson D C B" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_183.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line G H", "line G F", "line F E", "line E D", "line D C", "line B C", "line A B", "line H A" ], "circles": [], "semantics": [ "m \\angle GFE = 150", "m \\angle FED = 140", "m \\angle EDC = m \\angle HGF = 130", "m \\angle DCB = 100", "m \\angle CBA = m \\angle BAH = 145", "m \\angle GHA = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_184.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line F D", "line E F", "line E D", "line C A", "line A B", "line C B" ], "circles": [], "semantics": [ "m \\angle FDE = m \\angle CAB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_185.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B A", "line D E A", "line C D", "line C B", "line B E" ], "circles": [], "semantics": [ "DA \\perp BE on E", "CB = b_{1}", "BE = h", "AD = b_{2}" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_186.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C", "line D C", "line A D", "line B A", "line B E D", "line A E C" ], "circles": [], "semantics": [ "AE = 2", "BE = DE = 3", "CE = 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_187.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "P" ], "lines": [ "line Q P" ], "circles": [ "\\odot Q lieson P" ], "semantics": [ "QP = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_188.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "J", "K", "I", "H" ], "lines": [ "line G H I", "line G K J", "line K H" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_189.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "G", "A", "B", "C", "D", "E" ], "lines": [ "line C D G", "line F G", "line A F", "line A B C", "line B E", "line E D" ], "circles": [], "semantics": [ "CB = x-2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_190.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line B C D", "line A B", "line A C" ], "circles": [], "semantics": [ "BD \\perp AC on C", "AD = 12", "AC = x", "m \\angle ADC = m \\angle CBA = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_191.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "A", "C", "E", "R" ], "lines": [ "line A C", "line C E", "line P E", "line A P", "line A R E", "line P R C" ], "circles": [], "semantics": [ "EP = 7.47", "AR = 3.5", "CR = 6.6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_192.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "F" ], "lines": [ "line B C", "line D C", "line A D", "line A B", "line A F C", "line B F D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_193.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "X", "R", "Y", "Z", "O" ], "lines": [ "line P X Q", "line Q Y R", "line P Z R" ], "circles": [ "\\odot O lieson X Y Z" ], "semantics": [ "PX = 15", "RZ = 17" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_194.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "A", "E" ], "lines": [ "line A E C", "line B C", "line B D A", "line D E" ], "circles": [], "semantics": [ "ED = 2x", "BC = x+12", "BD = AD" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_195.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "P", "B", "C", "D", "E" ], "lines": [ "line A B D", "line A C E", "line C P", "line P B" ], "circles": [], "semantics": [ "AE \\perp CP on C", "CP = BP = 7" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_196.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "E", "F", "B", "D" ], "lines": [ "line C B", "line A B", "line A C", "line F E", "line D E", "line D F" ], "circles": [], "semantics": [ "CB \\perp AC on C", "FE \\perp DF on F", "AC = 21", "CB = 27", "FE = 18", "DF = x", "m \\angle BAC = m \\angle EDF" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_197.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line D B E G", "line a lieson A B C", "line b lieson F E H" ], "circles": [], "semantics": [ "m \\angle EBC = 88", "m \\angle BEH = 4x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_198.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "E", "F" ], "lines": [ "line C D A", "line C E B", "line A F B" ], "circles": [ "\\odot A lieson D F", "\\odot C lieson E D", "\\odot B lieson F E" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_199.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line B F", "line F E", "line E D", "line C D", "line A C" ], "circles": [], "semantics": [ "AB = AC = CD = BF = FE = DE" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_200.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line A C", "line A B" ], "circles": [], "semantics": [ "AC \\perp AB on A", "BA = 5", "CA = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_201.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "J", "A", "B", "C", "D" ], "lines": [ "line B A", "line A D", "line D C", "line B C", "line B J D" ], "circles": [ "\\odot J lieson B A D C" ], "semantics": [ "DC \\perp BC on C", "CB = 9" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_202.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "E", "F" ], "lines": [ "line G F", "line E F", "line G E" ], "circles": [], "semantics": [ "GE = 4.3", "GF = 8.2", "m \\angle FEG = 85", "m \\angle GFE = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_203.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "D", "B", "A", "E" ], "lines": [ "line D E B", "line D A", "line C B", "line C E A", "line D C" ], "circles": [], "semantics": [ "DA \\parallel CB", "CB = 6x-4", "DA = 3x+1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_204.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line E D", "line F D", "line F E", "line B C", "line A C", "line B A" ], "circles": [], "semantics": [ "m \\angle DEF = m \\angle CBA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_205.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C B", "line A B", "line A C" ], "circles": [], "semantics": [ "AB \\perp AC on A", "AC = x", "BA = 15", "BC = y", "m \\angle BCA = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_206.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line D C", "line B C", "line A B" ], "circles": [], "semantics": [ "AD \\parallel BC", "BC \\perp AB on B", "m \\angle ADC = x", "m \\angle DCB = x-50" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_207.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C", "line C E", "line B E", "line A B", "line A D E", "line C D B" ], "circles": [], "semantics": [ "CE = BE", "m \\angle ACD = y", "m \\angle ECD = z", "m \\angle CAD = 25", "m \\angle BED = 35", "m \\angle ADC = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_208.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "S", "U", "Y", "Z", "T" ], "lines": [ "line Y Z", "line T U", "line S T", "line S U", "line X Y", "line X Z" ], "circles": [], "semantics": [ "XY = 20", "XZ = 22", "ST = 4t", "TU = 24", "US = t^{2}-3", "ZY = 5t-1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_209.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D A", "line A B", "line C B", "line D C" ], "circles": [], "semantics": [ "DA \\perp AB on A", "AB \\perp CB on B", "DA = CD = 10", "BC = 16" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_210.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "F", "D", "E" ], "lines": [ "line C F", "line C D", "line D E", "line E F", "line A F", "line B A", "line B C" ], "circles": [], "semantics": [ "BA = DE", "m \\angle FCB = m \\angle FCD = 60", "m \\angle CFA = m \\angle CFE = 50", "m \\angle ABC = m \\angle CDE = 120", "m \\angle FAB = m \\angle DEF = 130" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_211.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D C A", "line B A", "line C B" ], "circles": [], "semantics": [ "DA \\perp BA on A", "m \\angle DCB = 123", "m \\angle ABC = m \\angle 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_212.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "A", "J", "D", "K", "Z" ], "lines": [ "line D Z K", "line F A J", "line A Z", "line J K" ], "circles": [], "semantics": [ "JK = 7.1", "DZ = ZK" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_213.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C A", "line A B", "line C B" ], "circles": [], "semantics": [ "AB \\perp CB on B", "CA = x", "AB = 15", "m \\angle CAB = 70" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_214.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B D", "line A C E" ], "circles": [ "\\odot F lieson B D E C" ], "semantics": [ "BD = 20", "AB = 11", "AC = 13", "CE = c" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_215.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Y", "R", "K", "Z", "P" ], "lines": [ "line R K Z", "line Y K P", "line R P", "line Y Z", "line R Y", "line P Z" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_216.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "L", "K", "M", "J" ], "lines": [ "line K J M", "line L M", "line L J", "line L K" ], "circles": [], "semantics": [ "LK = LJ = JM", "m \\angle MLJ = m \\angle 2", "m \\angle MJL = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_217.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line g lieson B E F", "line C D E H", "line f lieson A D G" ], "circles": [], "semantics": [ "line f \\parallel line g", "m \\angle CDA = m \\angle 1", "m \\angle EDA = m \\angle 2", "m \\angle CDG = m \\angle 3", "m \\angle BED = m \\angle 5", "m \\angle EDG = m \\angle 4", "m \\angle BEH = m \\angle 6", "m \\angle FED = m \\angle 7", "m \\angle FEH = m \\angle 8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_218.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C D", "line A C E" ], "circles": [], "semantics": [ "m \\angle BCA = 6x", "m \\angle BCE = 11y", "m \\angle DCE = 4x+16" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_219.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "R", "S", "T", "Q", "A", "B", "C", "D" ], "lines": [ "line A P Q R B", "line C T Q", "line D S Q" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_220.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C D E", "line B F E", "line B D", "line B C", "line B A", "line F A", "line A E" ], "circles": [], "semantics": [ "CE \\perp BD on D", "BE \\perp FA on F", "ED = 15", "CD = 7.5", "BA = x", "AF = 2.7", "CB = 11.6", "AE = 13" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_221.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C D", "line B A", "line B D", "line B C" ], "circles": [], "semantics": [ "AD \\perp BC on C", "BA = 5.7", "BD = 5", "BC = AC = 4", "DC = 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_222.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "D", "A", "B", "E", "F", "G", "H", "I", "J", "K", "L", "M" ], "lines": [ "line C E A B D", "line j lieson L F A H J", "line k lieson K G A I M" ], "circles": [ "\\odot C lieson F E I", "\\odot D lieson B G H" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_223.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line C D E", "line B E", "line G F H", "line A H", "line B C", "line B D", "line A G", "line A F" ], "circles": [], "semantics": [ "GH \\perp AF on F", "CE \\perp BD on D", "BE = 26.2", "HA = x", "BD = 17.3", "FA = 24.22", "m \\angle DCB = m \\angle FGA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_224.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C E", "line B D", "line B A", "line D E", "line B C" ], "circles": [], "semantics": [ "AE \\perp BC on C", "AE \\perp DE on E", "DE = BC = AC = h", "EC = b" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_225.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "S", "U", "T", "Q", "R", "A", "B", "C", "D" ], "lines": [ "line B S R", "line S T", "line C Q R", "line T U A" ], "circles": [ "\\odot D lieson S T R" ], "semantics": [ "m \\angle SRQ = 71", "m \\widehat ST = 166" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_226.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line E A", "line A B C", "line D C", "line D B", "line E B" ], "circles": [], "semantics": [ "AC \\perp DC on C", "m \\angle AEB = 56", "m \\angle DBE = 50", "m \\angle EAB = 45", "m \\angle CDB = m \\angle 3", "m \\angle ABE = m \\angle 1", "m \\angle CBD = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_227.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line A B", "line B C" ], "circles": [], "semantics": [ "AC = 8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_228.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line D C B", "line A D", "line A C" ], "circles": [], "semantics": [ "DB \\perp AC on C", "AB = s", "CD = \\frac{s}{2}" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_229.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line C A", "line C B" ], "circles": [], "semantics": [ "BA \\perp CB on B", "m \\angle CAB = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_230.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B A", "line F B", "line F A", "line C D", "line C E", "line D E" ], "circles": [], "semantics": [ "BA \\perp FA on A", "CD \\perp DE on D", "BA = DE", "m \\angle ABF = m \\angle 1", "m \\angle CED = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_231.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "H", "K", "G", "J" ], "lines": [ "line F K", "line H J K", "line H G F", "line G J" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_232.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line B D", "line A D C", "line B A" ], "circles": [], "semantics": [ "BD \\perp AC on D", "AB = x", "BC = 10", "BD = 6", "AC = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_233.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "P", "O", "Q", "N" ], "lines": [ "line P O", "line Q N", "line M Q P", "line M N O" ], "circles": [], "semantics": [ "QN \\parallel PO", "PQ = x", "ON = 3\\frac{3}{5}", "MQ = 5", "MN = 6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_234.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line G A D L", "line H B C K", "line I B A F" ], "circles": [], "semantics": [ "m \\angle HBI = m \\angle 16", "m \\angle DAF = m \\angle 2", "m \\angle CBA = m \\angle 10", "m \\angle FAG = m \\angle 1", "m \\angle HBA = m \\angle 9", "m \\angle DAB = m \\angle 7", "m \\angle CBI = m \\angle 15", "m \\angle GAB = m \\angle 8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_235.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "P", "N", "Q", "A" ], "lines": [ "line M N", "line P Q" ], "circles": [ "\\odot A lieson M N Q P" ], "semantics": [ "MN = 26", "PQ = 3x+5", "l \\widehat MN = l \\widehat PQ" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_236.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line E F G", "line G A B", "line B C D", "line E A D", "line F A C" ], "circles": [], "semantics": [ "CA = y-20", "FA = 36", "EA = 48", "DA = y", "EF = FG" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_237.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "G" ], "lines": [ "line B G C", "line B D", "line A G D", "line B A", "line A C", "line D C" ], "circles": [], "semantics": [ "BC \\perp AD on G", "BA = BD = AC = DC" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_238.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A D E", "line B C E", "line B A", "line C D" ], "circles": [], "semantics": [ "AE \\perp BA on A", "AE \\perp CD on D", "BC = 4x+2", "AD = 3y+5", "ED = 7y-11", "EC = BC = 6x-10" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_239.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "G", "E", "F", "H", "D" ], "lines": [ "line A G B", "line E H B", "line E D F", "line A H F", "line C D H G", "line C F B", "line C E A" ], "circles": [], "semantics": [ "AB \\perp CG on G", "BG = AG = 8", "BF = 9.9", "GH = 6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_240.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "N", "J", "L", "M", "K" ], "lines": [ "line N K L", "line J K M", "line L M", "line J N" ], "circles": [], "semantics": [ "JK = KM", "m \\angle KLM = m \\angle KNJ" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_241.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line n lieson A E F G", "line k lieson B E H", "line j lieson C F I", "line D E" ], "circles": [], "semantics": [ "line k \\perp DE on E", "m \\angle GFC = 135", "m \\angle AED = m \\angle 2 = m \\angle AEB = m \\angle 1", "m \\angle HED = m \\angle 3", "m \\angle EFC = m \\angle 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_242.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "O" ], "lines": [ "line A B", "line B C", "line A C", "line A D", "line C D" ], "circles": [ "\\odot O lieson B C D A" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_243.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J" ], "lines": [ "line A B E", "line C E I", "line G I J", "line D G H", "line F D B" ], "circles": [], "semantics": [ "m \\angle GDF = m \\angle 4", "m \\angle IGH = m \\angle 5", "m \\angle EIJ = m \\angle 1", "m \\angle BEC = m \\angle 2", "m \\angle ABD = m \\angle 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_244.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line E A D", "line C D", "line B C", "line B E", "line B A" ], "circles": [], "semantics": [ "ED \\perp BA on A", "BC = 14", "DC = 26", "m \\angle EBA = 30" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_245.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line A B", "line A C" ], "circles": [], "semantics": [ "BA = AC = 9", "m \\angle CAB = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_246.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line F B", "line E C", "line C D" ], "circles": [], "semantics": [ "m \\angle ABF = m \\angle 1 = m \\angle ECD = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_247.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "W", "V", "A", "B", "C", "D" ], "lines": [ "line B W", "line W A", "line C V", "line D V" ], "circles": [], "semantics": [ "m \\angle BWA = m \\angle CVD" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_248.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D B", "line D A", "line D C", "line C B", "line A B" ], "circles": [], "semantics": [ "m \\angle BDC = 27", "m \\angle DCB = m \\angle 1", "m \\angle DBC = m \\angle 2", "m \\angle DBA = m \\angle 3", "m \\angle BDA = m \\angle 5", "m \\angle DAB = m \\angle 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_249.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line A D", "line B A", "line C D" ], "circles": [], "semantics": [ "m \\angle CBA = m \\angle ADC" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_250.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "S", "P", "A", "B" ], "lines": [ "line A R S B", "line R P", "line S P" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_251.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "J", "G", "K", "M" ], "lines": [ "line J G", "line J K", "line M K", "line G M", "line G K" ], "circles": [], "semantics": [ "JG = GM" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_252.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B", "E", "F" ], "lines": [ "line F D", "line E C", "line B A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_253.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line B C", "line A C" ], "circles": [], "semantics": [ "m \\angle ABC = 117", "m \\angle BCA = 33", "m \\angle BAC = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_254.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "W", "R", "Z", "S", "T" ], "lines": [ "line R Z T", "line S Z W", "line R W", "line S T", "line R S", "line W T" ], "circles": [], "semantics": [ "RW \\perp RS on R" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_255.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "S", "P", "Q" ], "lines": [ "line Q P", "line S P", "line S Q", "line R Q", "line R S" ], "circles": [], "semantics": [ "m \\angle QSR = m \\angle PSQ = m \\angle SQR = m \\angle PQS" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_256.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A C", "line B C", "line D E", "line D F", "line B A", "line E F" ], "circles": [], "semantics": [ "BC \\perp BA on B", "DF \\perp EF on F", "CA = 39", "DF = 24", "CB = 2x-4", "DE = x+6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_257.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C D", "line D A", "line C A", "line B A" ], "circles": [], "semantics": [ "DA = 6", "DC = 4", "AB = x+3", "BC = x", "m \\angle DAC = m \\angle CAB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_258.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "D", "A", "B", "E", "F", "G" ], "lines": [ "line A F E G B", "line C E D" ], "circles": [ "\\odot A lieson C G D", "\\odot B lieson F C D" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_259.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B D", "line C B", "line C D", "line A D" ], "circles": [ "\\odot A lieson C D B" ], "semantics": [ "AD = 1.5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_260.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line l lieson C K L F", "line m lieson B J I G", "line a lieson D K J A", "line b lieson E L I H" ], "circles": [], "semantics": [ "m \\angle CKD = m \\angle 1", "m \\angle LKD = m \\angle 2", "m \\angle KLE = m \\angle 3", "m \\angle FLE = m \\angle 4", "m \\angle CKJ = m \\angle 8", "m \\angle LKJ = m \\angle 7", "m \\angle KLI = m \\angle 6", "m \\angle FLI = m \\angle 5", "m \\angle BJK = m \\angle 9", "m \\angle IJK = m \\angle 10", "m \\angle JIL = m \\angle 11", "m \\angle GIL = m \\angle 12", "m \\angle BJA = m \\angle 16", "m \\angle JIH = m \\angle 14", "m \\angle IJA = m \\angle 15", "m \\angle GIH = m \\angle 13" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_261.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "S", "T", "U", "A" ], "lines": [ "line R S", "line U T" ], "circles": [ "\\odot A lieson R S T U" ], "semantics": [ "l \\widehat SR = l \\widehat TU", "m \\widehat SR = 3x", "m \\widehat TU = 2x+27" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_262.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line B C", "line D C", "line A D", "line A C" ], "circles": [], "semantics": [ "DC = BC", "m \\angle BCA = 38", "m \\angle DCA = 41" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_263.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "G", "C", "A", "E", "F", "D", "H" ], "lines": [ "line B C G", "line G E", "line B F E", "line A F D G" ], "circles": [ "\\odot H lieson B C D E A" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_264.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B C", "line A B", "line A C", "line F D", "line D E", "line F E" ], "circles": [], "semantics": [ "FE = 18", "AC = 10" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_265.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "G", "E", "H" ], "lines": [ "line E H", "line F G", "line F E", "line G H" ], "circles": [], "semantics": [ "FG \\parallel EH", "m \\angle HEF = 12z^{2}", "m \\angle EHG = 7z^{2}+20" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_266.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C B", "line A B", "line C A" ], "circles": [], "semantics": [ "AC = 3.0", "BA = 1.2", "CB = x", "m \\angle CAB = 123" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_267.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B A C", "line E A", "line F A", "line D A" ], "circles": [ "\\odot A lieson F E D C B" ], "semantics": [ "m \\angle EAF = 3x-16", "m \\angle EAD = 2x+9" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_268.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "E", "F", "G", "H", "I" ], "lines": [ "line m lieson H C F", "line B C G", "line B A D", "line l lieson I A E" ], "circles": [], "semantics": [ "line l \\parallel line m", "m \\angle BCH = 33", "m \\angle BAI = 38" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_269.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "S", "V", "T", "U" ], "lines": [ "line T S", "line T V", "line V U", "line T U", "line S U" ], "circles": [], "semantics": [ "TV \\parallel SU", "TS = TU = VU" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_270.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "L", "K", "R", "J", "A" ], "lines": [ "line L A K", "line A J", "line J R" ], "circles": [ "\\odot J lieson L R K" ], "semantics": [ "LK \\perp AJ on A", "AJ = x", "JR = LK = 10" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_271.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "R", "P" ], "lines": [ "line Q P", "line P R" ], "circles": [ "\\odot P lieson Q R" ], "semantics": [ "PR = 15", "m \\angle RPQ = 120" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_272.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "U", "R", "S", "T", "Q", "A", "B", "C" ], "lines": [ "line C T S", "line A Q S", "line R Q T", "line B R S", "line U R", "line U T" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_273.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line D C B", "line A B E", "line C E F" ], "circles": [], "semantics": [ "m \\angle DCE = z", "m \\angle BCE = x", "m \\angle CBE = w", "m \\angle BEC = y", "m \\angle CBA = z-13", "m \\angle BEF = z+10" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_274.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C D", "line B D", "line A B", "line A C" ], "circles": [], "semantics": [ "BD \\perp AB on B", "AB \\perp AC on A", "CD \\perp AC on C", "CD \\perp BD on D", "BA = 22", "AC = 17" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_275.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line a lieson B F", "line b lieson E G C", "line A F G D" ], "circles": [], "semantics": [ "line b \\perp AD on G" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_276.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "C", "R", "A", "S", "T" ], "lines": [ "line S T", "line R T", "line R S", "line C B", "line B A", "line C A" ], "circles": [], "semantics": [ "CB = y+13", "ST = 2y-8", "m \\angle ABC = 3x+40", "m \\angle TSR = 5x+20" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_277.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B C", "line B A" ], "circles": [], "semantics": [ "AB = 32", "CB = x", "m \\angle CBA = 73", "m \\angle BAC = 51" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_278.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P" ], "lines": [ "line A M N O B", "line C M L H", "line D N K I", "line E O P J" ], "circles": [], "semantics": [ "CH \\parallel DI \\parallel EJ", "NO = x", "MN = 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_279.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "J", "H", "K", "A", "B", "C", "D" ], "lines": [ "line C K A" ], "circles": [ "\\odot D lieson J K H" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_280.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line A C", "line B C" ], "circles": [], "semantics": [ "AC = x", "CB = 23", "BA = 27", "m \\angle ABC = 36" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_281.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "R", "T", "Q", "S", "A", "B", "C", "D" ], "lines": [ "line B T Q R D", "line A S Q", "line C P Q" ], "circles": [], "semantics": [ "AQ \\perp CQ on Q", "m \\angle RQP = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_282.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "F", "E", "D", "P" ], "lines": [ "line A P D", "line B D C", "line B E A", "line A F C", "line E P C", "line B P F" ], "circles": [], "semantics": [ "BE = EA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_PGDPHW_283.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M" ], "lines": [ "line A C F I", "line A D G H", "line K F B", "line B G L", "line E F J", "line E G M" ], "circles": [ "\\odot B lieson E C F G D" ], "semantics": [ "m \\angle FBG = m \\angle 1", "m \\angle FEG = m \\angle 2", "m \\widehat DC = y", "m \\widehat GF = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_284.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Y", "K", "X", "L", "Z", "J" ], "lines": [ "line Y Z", "line X Y", "line X Z", "line K J", "line K L", "line J L" ], "circles": [], "semantics": [ "KL = x", "YZ = 15", "YX = 5", "m \\angle JKL = m \\angle XYZ = 51", "m \\angle ZXY = m \\angle LJK" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_285.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line q lieson G C D L", "line m lieson J A D E", "line l lieson I B C F", "line p lieson H B A K" ], "circles": [], "semantics": [ "m \\angle CDE = m \\angle 15", "m \\angle BCD = m \\angle 10", "m \\angle FCD = m \\angle 14", "m \\angle GCB = m \\angle 9", "m \\angle LDA = m \\angle 12", "m \\angle CDA = m \\angle 11", "m \\angle JAB = m \\angle 3", "m \\angle EDL = m \\angle 16", "m \\angle DAB = m \\angle 7", "m \\angle IBA = m \\angle 2", "m \\angle CBA = m \\angle 6", "m \\angle DAK = m \\angle 8", "m \\angle GCF = m \\angle 13", "m \\angle JAK = m \\angle 4", "m \\angle HBI = m \\angle 1", "m \\angle HBC = m \\angle 5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_286.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "H", "A", "C", "B" ], "lines": [ "line D H", "line D A", "line H A", "line H C", "line D C", "line D B", "line H B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_287.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "T", "S", "V", "U", "W" ], "lines": [ "line R T", "line T S", "line R S", "line W V", "line W U", "line V U" ], "circles": [], "semantics": [ "RT = y+3", "VU = 21", "WU = 29", "VW = 20", "SR = x", "TS = 49", "m \\angle UVW = m \\angle RTS" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_288.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "S", "Q", "R", "A", "B" ], "lines": [ "line P Q", "line Q A S", "line S R", "line P A R" ], "circles": [ "\\odot B lieson P Q R S" ], "semantics": [ "m \\angle QPA = 45", "m \\angle SRA = 40", "m \\angle ASR = x", "m \\angle PQA = y" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_289.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line B C", "line A C" ], "circles": [ "\\odot D lieson B C A" ], "semantics": [ "m \\angle BAC = 2x", "m \\widehat AB = 6v", "m \\widehat CB = 6y", "m \\widehat AC = 4x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_290.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "S", "Y", "T", "Z", "U", "V", "W", "X" ], "lines": [ "line S T", "line T Z", "line Y Z", "line S Y", "line S U", "line U V", "line V X", "line W X", "line U W", "line X Z" ], "circles": [], "semantics": [ "YS = ZY = XZ = 7", "ST = UV = 8", "TZ = 6", "SU = XW = 4", "WU = 9", "VX = 5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_291.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "E", "F" ], "lines": [ "line A D E", "line A B", "line B C", "line D C F" ], "circles": [], "semantics": [ "m \\angle DAB = m \\angle 1", "m \\angle ABC = m \\angle 2", "m \\angle ADC = m \\angle 4", "m \\angle BCD = m \\angle 3", "m \\angle BCF = m \\angle 6", "m \\angle EDC = m \\angle 5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_292.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line B C D", "line H G F", "line C A", "line A G", "line A E" ], "circles": [ "\\odot A lieson B D E F H" ], "semantics": [ "BD \\perp CA on C", "HF \\perp AG on G", "BD = 9", "HG = GF = x", "CA = AG = 5", "AE = y" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_293.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "T", "S", "R" ], "lines": [ "line P T R", "line S R", "line Q R", "line Q T S", "line P S", "line P Q" ], "circles": [], "semantics": [ "PQ = PS" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_294.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B", "E" ], "lines": [ "line A E C", "line D E B", "line D C" ], "circles": [ "\\odot E lieson D C B A" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_295.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line C A", "line C B" ], "circles": [], "semantics": [ "BC = AC = 12", "m \\angle BCA = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_296.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "G", "E", "C" ], "lines": [ "line A E G", "line A C", "line E C", "line C G" ], "circles": [ "\\odot C lieson A G" ], "semantics": [ "AC = CG" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_297.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line C D", "line A D", "line B A" ], "circles": [], "semantics": [ "BC \\parallel AD", "m \\angle CBA = x+75", "m \\angle DAB = 2x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_298.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line F E", "line C B", "line E D", "line B A", "line F D", "line C A" ], "circles": [], "semantics": [ "BA = 18", "FE = 32", "ED = 24", "BC = y-3", "m \\angle BAC = m \\angle EDF" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_299.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line A C", "line B C", "line E F", "line F D", "line E D" ], "circles": [], "semantics": [ "m \\angle EDF = 3x+y", "m \\angle FED = 5x-y", "m \\angle CBA = m \\angle DFE = 148", "m \\angle BCA = 18" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_300.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "O", "H", "I", "F", "G", "N" ], "lines": [ "line H O", "line H G", "line O G", "line F N", "line F I", "line N I" ], "circles": [], "semantics": [ "HG = NF", "m \\angle FIN = m \\angle HGO" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_301.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "E" ], "lines": [ "line A D C", "line B E C", "line B A", "line B D", "line E D" ], "circles": [], "semantics": [ "BC \\perp BA on B", "AC \\perp ED on D", "BA = BD = AD = DC" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_302.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "S", "R", "T", "Q" ], "lines": [ "line S R Q", "line P R T", "line P Q", "line S T" ], "circles": [], "semantics": [ "PR = QR", "m \\angle RPQ = 56" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_303.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Y", "B", "X", "Z", "C", "A" ], "lines": [ "line X Z", "line Y Z", "line B C", "line Y X", "line B A", "line A C" ], "circles": [], "semantics": [ "YZ = 2x^{2}", "XZ = CA = 82", "BC = x^{2}+36", "m \\angle XZY = m \\angle BCA = 42" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_304.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "R", "T", "S" ], "lines": [ "line Q T", "line Q R", "line R S", "line T S" ], "circles": [], "semantics": [ "RS = 6x+8", "TQ = \\frac{1}{2}(14x+8)" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_305.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "K", "J", "N", "M", "Q" ], "lines": [ "line N Q K", "line J N", "line N M", "line K M", "line J Q M", "line J K" ], "circles": [], "semantics": [ "JN \\perp JK on J", "NM \\perp KM on M" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_306.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D" ], "lines": [ "line B C", "line A D", "line B A", "line C D" ], "circles": [], "semantics": [ "BC \\parallel AD", "BA = CD", "m \\angle BCD = 74" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_307.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "A", "B", "D", "C" ], "lines": [ "line E D", "line A B" ], "circles": [ "\\odot C lieson A B D E" ], "semantics": [ "AB = ED = 7", "m \\widehat AB = 105", "m \\widehat ED = 5x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_308.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line B C", "line B A", "line A D", "line C D" ], "circles": [], "semantics": [ "m \\angle CAB = 26", "m \\angle CBA = m \\angle 2", "m \\angle ACB = m \\angle 1", "m \\angle ADC = m \\angle 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_309.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "K", "J", "L" ], "lines": [ "line K L", "line K J", "line J L" ], "circles": [], "semantics": [ "KJ \\perp JL on J", "LJ = 12", "KJ = LJ = x^{2}+4x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_310.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A E D", "line B E C", "line B D", "line D C", "line A C", "line B A" ], "circles": [], "semantics": [ "BE = 11", "AE = 13" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_311.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line F E", "line D E", "line C D", "line B C", "line H B", "line H G", "line G F", "line A H", "line A B" ], "circles": [], "semantics": [ "m \\angle BHA = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_312.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Z", "W", "X", "Y", "A", "A0", "A1" ], "lines": [ "line A X Z", "line A Y W" ], "circles": [ "\\odot A1 lieson X Y", "\\odot A0 lieson Z W" ], "semantics": [ "m \\angle XAY = 65" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_313.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C A", "line B A", "line C B" ], "circles": [], "semantics": [ "BA \\perp CB on B", "CA = 18", "CB = x", "AB = y", "m \\angle ACB = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_314.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "G", "H", "F", "K", "J", "E" ], "lines": [ "line D G H F", "line E J K F", "line D E", "line G J", "line H K" ], "circles": [], "semantics": [ "HF = 7", "DG = 2n-1", "DE = 2n+1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_315.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "P", "B", "C" ], "lines": [ "line A B", "line A C", "line P" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_316.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C D", "line B C E", "line B A", "line D E" ], "circles": [], "semantics": [ "BA \\parallel DE", "m \\angle CAB = 45", "m \\angle DCE = 35", "m \\angle CED = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_317.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "T", "Y" ], "lines": [ "line P Y", "line P T", "line T Y" ], "circles": [], "semantics": [ "PT \\perp TY on T", "TY = 41", "PT = 100" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_318.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line A C", "line B C" ], "circles": [], "semantics": [ "BA \\perp AC on A", "BA = 17\\sqrt{2}", "CB = x", "m \\angle BCA = m \\angle CBA = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_319.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "S", "R", "C", "A", "B", "D" ], "lines": [ "line S D Q", "line S C R", "line Q A R", "line Q B", "line S B", "line B C", "line D B", "line B A", "line B R" ], "circles": [ "\\odot B lieson S R Q" ], "semantics": [ "QR \\perp BA on A", "SQ \\perp DB on D", "SR \\perp BC on C", "QA = AR" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_320.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "Z", "Y", "W" ], "lines": [ "line X Z", "line Y W Z", "line X Y", "line X W" ], "circles": [], "semantics": [ "XY = 8", "XZ = 12.8", "ZW = t-2", "YW = \\frac{t}{2}", "m \\angle YXW = m \\angle ZXW" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_321.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "H", "L", "K", "M", "I", "O", "J", "N" ], "lines": [ "line K J", "line J I", "line H I", "line K H", "line O L", "line L M", "line N M", "line O N" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_322.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line G B F", "line F E I", "line H D I", "line G C H", "line B A", "line A E" ], "circles": [ "\\odot A lieson C B E D" ], "semantics": [ "BA \\perp AE on A" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_323.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line A B" ], "circles": [ "\\odot B lieson A C" ], "semantics": [ "m \\angle CBA = 90" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_324.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line C A", "line B A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_325.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line E D", "line D A C", "line B C", "line E B", "line B A" ], "circles": [], "semantics": [ "DC \\perp BC on C", "CB = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_326.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C B", "line C D A", "line B E A", "line D E" ], "circles": [], "semantics": [ "CB \\parallel DE", "CD = 10", "AD = x", "BE = 30", "BA = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_327.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D C B", "line D E", "line A C", "line A B", "line C E" ], "circles": [], "semantics": [ "DB \\perp CE on C", "DB \\perp AB on B", "DE = 12\\sqrt{3}", "AB = x", "BC = DC = y", "m \\angle DEC = 30", "m \\angle BCA = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_328.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "P", "B", "C" ], "lines": [ "line C P B", "line A P" ], "circles": [ "\\odot P lieson C A B" ], "semantics": [ "CB = 24", "m \\angle BPA = 118" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_329.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line D E C", "line A E B" ], "circles": [ "\\odot F lieson D A C B" ], "semantics": [ "EA = 8", "ED = x", "CE = 2x", "EB = 9" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_330.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "S", "Q", "P", "T" ], "lines": [ "line Q P", "line Q T S", "line S P", "line R Q", "line R T P", "line R S" ], "circles": [], "semantics": [ "ST = 2y+12", "PT = 5x-28", "RT = x", "QT = 5y" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_331.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "N", "L", "M", "R" ], "lines": [ "line L M", "line M R N", "line P N", "line L Q P", "line Q R" ], "circles": [], "semantics": [ "LM = 4x-10", "NP = 8", "QR = x+2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_332.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "Y", "Z", "P", "A", "C", "X" ], "lines": [ "line B Y A", "line A X C", "line B Z C", "line A P", "line B P", "line P C", "line P Z", "line Y P", "line P X" ], "circles": [], "semantics": [ "BC \\perp PZ on Z", "BA \\perp YP on Y", "AC \\perp PX on X" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_333.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line C A", "line B A" ], "circles": [], "semantics": [ "BC \\perp CA on C", "BC = x", "CA = 19", "m \\angle BAC = 24" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_334.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D" ], "lines": [ "line C B", "line A D B", "line C A", "line C D" ], "circles": [], "semantics": [ "AB \\perp CD on D", "CB = CA", "m \\angle ACD = m \\angle BCD" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_335.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "R", "S" ], "lines": [ "line Q P", "line P S R", "line Q R", "line Q S" ], "circles": [], "semantics": [ "PS = 18", "RS = QP = 24", "RQ = 32", "m \\angle RQS = m \\angle PQS" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_336.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C" ], "lines": [ "line C B", "line D A", "line D C", "line A B" ], "circles": [], "semantics": [ "m \\angle BCD = 2y-40", "m \\angle DAB = y+10", "m \\angle CBA = 4x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_337.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L" ], "lines": [ "line A B D F", "line C B L J", "line E D G I", "line K L G H" ], "circles": [], "semantics": [ "EI \\parallel CJ", "m \\angle DBC = 85", "m \\angle BLG = m \\angle 1", "m \\angle DGL = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_338.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C B A", "line C D", "line D A", "line D B" ], "circles": [], "semantics": [ "CD \\perp DA on D", "CA \\perp DB on B", "DA = 10", "DB = x", "CB = y", "AB = 4", "CA = z" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_339.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C E", "line B E", "line B A", "line F A E", "line E D" ], "circles": [ "\\odot A lieson B E D F" ], "semantics": [ "m \\angle BEA = a", "m \\angle AED = c", "m \\angle CEB", "m \\widehat DF = 84", "m \\widehat BF = 52" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_340.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line B C", "line C D", "line A D", "line B A" ], "circles": [], "semantics": [ "m \\angle BCD = m \\angle DAB = y", "m \\angle CBA = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_341.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B E", "line D E", "line C D", "line C B", "line A E" ], "circles": [ "\\odot A lieson C D E B" ], "semantics": [ "AE = 10" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_342.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line E F", "line D C", "line E D", "line F B C", "line A C", "line A B" ], "circles": [], "semantics": [ "FC \\perp AB on B", "CA = 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_343.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A E D", "line B C", "line B A", "line C D", "line C E" ], "circles": [], "semantics": [ "AD \\perp CE on E", "BC = 14", "BA = 7", "m \\angle EDC = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_344.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "E", "D", "S", "F", "G", "H" ], "lines": [ "line C D E F", "line S C", "line A B C" ], "circles": [ "\\odot G lieson A S B", "\\odot H lieson S E D" ], "semantics": [ "CB = 10", "DE = x", "CD = 9", "AB = 8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_345.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "A" ], "lines": [ "line A B C D" ], "circles": [], "semantics": [ "AD = 3\\frac{3}{4}", "AB = BC = CD" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_346.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D B A", "line D C E", "line E A", "line C B" ], "circles": [], "semantics": [ "CB \\parallel EA", "DB = 2y-1", "DC = x+3", "EC = \\frac{3}{2}x+2", "AB = DB = 3y-5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_347.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "E" ], "lines": [ "line B C", "line C A", "line B E A", "line E C" ], "circles": [], "semantics": [ "BA \\perp EC on E", "BC \\perp CA on C", "BC = a", "CA = b", "BE = x", "AE = y", "BA = c", "m \\angle EAC = 30", "m \\angle EBC = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_348.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line A C", "line A B" ], "circles": [], "semantics": [ "BC \\perp AB on B", "AB = 9", "BC = x", "CA = 15" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_349.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A C E", "line A B D" ], "circles": [ "\\odot F lieson D E C B" ], "semantics": [ "m \\angle CAB = 15", "m \\widehat BC = 2x", "m \\widehat DE = 80" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_350.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "T", "S", "R" ], "lines": [ "line R S", "line T S", "line T R" ], "circles": [], "semantics": [ "TR = 6", "RS = 5", "ST = 9" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_351.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line B G", "line G F", "line F E", "line D E", "line C D", "line B C", "line A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_352.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A D", "line D C", "line B C", "line A B" ], "circles": [], "semantics": [ "BA = DC = 4", "AD = CB = 7", "m \\angle CBA = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_353.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C B A" ], "circles": [ "\\odot D lieson A C" ], "semantics": [ "AC = 20" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_354.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "O", "E", "A", "B", "C", "D", "F", "G", "H", "I", "J" ], "lines": [ "line F A O", "line O E G", "line O B H", "line O C I", "line O D J" ], "circles": [], "semantics": [ "m \\angle AOB = 60", "m \\angle COD = 45", "m \\angle EOD = 25", "m \\angle BOC = 20" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_355.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B A", "line B C", "line C D", "line B D", "line A D" ], "circles": [], "semantics": [ "BA = CD", "m \\angle ABD = m \\angle CDB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_356.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "X", "Z", "Y", "T" ], "lines": [ "line C Y A", "line C Z B", "line A X B", "line A T Z", "line C T X", "line Y T B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_357.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line F G", "line H G", "line D H", "line C D", "line A C", "line A B", "line E B", "line E F" ], "circles": [], "semantics": [ "BA = 5", "EF = 32", "FG = 24", "EB = 10", "HD = 6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_358.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C D", "line A C", "line A B" ], "circles": [], "semantics": [ "m \\angle CBA = x", "m \\angle BCA = y", "m \\angle CAB = 60", "m \\angle DCA = 120" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_359.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "J", "K", "E", "C", "D" ], "lines": [ "line K J E", "line B A", "line C D", "line B K C", "line A E", "line E D", "line J C", "line B J" ], "circles": [ "\\odot J lieson B A E D C" ], "semantics": [ "KE \\perp BC on K", "AB = 5.88", "KJ = 4.05", "JC = 5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_360.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C E", "line D E", "line B E", "line B C D", "line A D", "line B A" ], "circles": [], "semantics": [ "BC = DC = 5", "EC = 8", "CA = 3", "BA = AD" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_361.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P" ], "lines": [ "line F G I K", "line E D L M", "line A B N O", "line H G D B C", "line J I L N P" ], "circles": [], "semantics": [ "FK \\parallel AO \\parallel EM", "DB = 4x+3", "DG = 7x-2", "LI = NL = 8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_362.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "E", "D" ], "lines": [ "line A E C", "line B D C", "line B A", "line D E" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_363.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C" ], "lines": [ "line A C", "line B C", "line B A" ], "circles": [], "semantics": [ "AC \\perp BA on A", "CB = 14", "m \\angle CBA = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_364.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line A F", "line B F", "line B G", "line F G", "line C F", "line E F", "line C E", "line C B", "line A B", "line C A", "line C D", "line D B" ], "circles": [], "semantics": [ "CA = AB = AF", "m \\angle FAC = m \\angle FAB = m \\angle BAC = 120" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_365.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "E", "F", "G" ], "lines": [ "line B D E", "line G A B", "line B C F" ], "circles": [], "semantics": [ "m \\angle ABC = 55", "m \\angle DBA = m \\angle DBC" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_366.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "E", "D", "F" ], "lines": [ "line B F E", "line C F A", "line F D" ], "circles": [ "\\odot F lieson B C D E A" ], "semantics": [ "BE \\perp FD on F", "m \\angle AFE = 63" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_367.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C E A", "line B D A" ], "circles": [ "\\odot F lieson B D E C" ], "semantics": [ "m \\angle DAE = 3x", "m \\widehat ED = 30", "m \\widehat CB = 4x+50" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_368.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line D C", "line C B", "line D B", "line E A", "line E F", "line F A" ], "circles": [], "semantics": [ "EF = x", "DC = 2.8", "BD = 4", "CB = 3.1", "FA = 12", "AE = 9.3", "m \\angle CDB = m \\angle EFA = 51", "m \\angle FAE = 44", "m \\angle DCB = 85" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_369.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C D", "line B D", "line B A", "line B C" ], "circles": [], "semantics": [ "BD \\perp BA on B", "AD \\perp BC on C", "BA = z", "AC = 2", "BC = x", "DC = 10", "DB = y" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_370.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C" ], "lines": [ "line A D", "line B C D", "line A B", "line A C" ], "circles": [], "semantics": [ "BD \\perp AC on C", "AD \\perp AB on A", "DC = 3", "AC = 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_371.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "D", "F", "E", "H" ], "lines": [ "line F E", "line D E", "line F H D", "line G F", "line G H E" ], "circles": [], "semantics": [ "DE = GF", "m \\angle HFG = m \\angle DEH = m \\angle EFH = m \\angle FEH" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_372.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D E C", "line B C", "line D A B", "line A E" ], "circles": [], "semantics": [ "DA = 2", "DE = y", "CB = 7", "BA = 3", "CE = 2.4", "AE = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_373.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B E", "line B C D" ], "circles": [ "\\odot A lieson C E D" ], "semantics": [ "EB = x", "BC = 4", "DC = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_374.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "A", "B", "C" ], "lines": [ "line B A", "line C A" ], "circles": [ "\\odot R lieson C B" ], "semantics": [ "BA = 5x-8", "AC = 3x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_PGDPHW_375.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C D", "line A C E" ], "circles": [], "semantics": [ "m \\angle DCA = m \\angle 1", "m \\angle BCA = m \\angle 4", "m \\angle DCE = m \\angle 2", "m \\angle BCE = m \\angle 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_376.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line C B", "line C D", "line D A", "line B A" ], "circles": [], "semantics": [ "CB = 3y-2", "CD = 2x-4", "DA = 4y-8", "BA = x+4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_377.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M" ], "lines": [ "line G L F", "line E K F", "line D M E", "line C A D", "line C I H", "line H J G", "line A B L" ], "circles": [ "\\odot B lieson I A M K L J" ], "semantics": [ "LA = 20" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_378.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line D E C", "line B A D" ], "circles": [ "\\odot F lieson A E" ], "semantics": [ "m \\angle ADE = 35", "m \\widehat AE = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_379.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "L", "J", "K", "N" ], "lines": [ "line J K", "line L K", "line M L", "line M J", "line M N K", "line J N L" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_380.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A B", "line D A C", "line A E" ], "circles": [ "\\odot A lieson D E C B" ], "semantics": [ "DC \\perp AE on A", "m \\angle BAD = 150", "m \\angle BAC = x", "m \\angle DAE = 85" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_381.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "F", "C", "D" ], "lines": [ "line A B", "line A C", "line B C", "line D F", "line D E", "line F E" ], "circles": [], "semantics": [ "AC = AB", "m \\angle BAC = m \\angle FDE" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_382.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C D", "line E D", "line F E", "line B F", "line B C", "line A E" ], "circles": [ "\\odot A lieson B F E D C" ], "semantics": [ "AE = 7", "BF = BC = CD = ED = FE" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_383.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "S", "W", "T", "R" ], "lines": [ "line T W", "line W R", "line S R", "line T S" ], "circles": [], "semantics": [ "TS = WR", "m \\angle WRS = 5x", "m \\angle RST = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_384.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "E" ], "lines": [ "line A E", "line E D", "line E C" ], "circles": [ "\\odot E lieson B C D A" ], "semantics": [ "m \\angle DEC = 65", "m \\angle AED = 80" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_385.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line D A H", "line B A F", "line I A E", "line C A G" ], "circles": [ "\\odot A lieson D C B I H G F E" ], "semantics": [ "BF = 16" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_386.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line C B", "line C A" ], "circles": [], "semantics": [ "AB \\perp CB on B", "AB = x", "CA = y", "BC = 6\\sqrt{3}", "m \\angle CAB = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_387.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "E", "D", "G", "A", "B" ], "lines": [ "line F A D", "line E A G" ], "circles": [ "\\odot B lieson E F G D" ], "semantics": [ "m \\angle DAG = m \\angle 3", "m \\widehat DG = 74", "m \\widehat FE = 90" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_388.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B" ], "lines": [ "line A C", "line B C" ], "circles": [ "\\odot C lieson A B" ], "semantics": [ "BC = 11", "m \\widehat AB = 60" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_389.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "F", "D", "E", "G", "H", "I", "J", "K", "L" ], "lines": [ "line G A B L", "line A C H", "line A D I", "line B E J", "line B F K" ], "circles": [], "semantics": [ "m \\angle LBF = 86", "m \\angle CAD = 33", "m \\angle EBF = 35", "m \\angle BAD = 87" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_390.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "N", "P", "O", "Q", "A" ], "lines": [ "line N A P", "line O N", "line P Q", "line N Q", "line O P", "line O A Q" ], "circles": [], "semantics": [ "PA = 3y-1", "OA = 4x-2", "NA = y+5", "QA = x+10" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_391.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line A C", "line B C" ], "circles": [], "semantics": [ "AB = 20", "AC = 14", "m \\angle ACB = 101" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_392.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "J", "P", "S", "M", "A", "B", "C" ], "lines": [ "line J S C", "line J P A", "line J M B", "line M S", "line S P" ], "circles": [], "semantics": [ "JB \\perp MS on M", "JA \\perp SP on P", "MS = 3x+5", "PS = 6x-7", "m \\angle SJM = m \\angle SJP" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_393.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "P", "R", "S", "A", "B", "C" ], "lines": [ "line Q S B", "line Q P A", "line Q R C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_394.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "F", "E", "B", "D" ], "lines": [ "line C E F", "line A D F", "line A B C", "line B D", "line D E" ], "circles": [], "semantics": [ "m \\angle DAB = m \\angle 1", "m \\angle ABD = m \\angle 2", "m \\angle ADB = m \\angle 5", "m \\angle CBD = m \\angle 3", "m \\angle BDE = m \\angle 6", "m \\angle FDE = m \\angle 7", "m \\angle ECB = m \\angle 4", "m \\angle CED = m \\angle 8", "m \\angle FED = m \\angle 9", "m \\angle EFD = m \\angle 10" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_PGDPHW_395.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B C", "line D C", "line A D", "line D B" ], "circles": [], "semantics": [ "AD = 2x+1", "AB = 7", "CB = x", "CD = 15", "m \\angle BDA = m \\angle CDB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_396.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line C F B", "line D E A", "line B A", "line F E", "line C D" ], "circles": [ "\\odot G lieson C D", "\\odot H lieson B A" ], "semantics": [ "DA \\perp FE on E", "EF = 16", "DA = 33" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_397.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line E D", "line A B D", "line A C", "line E B C" ], "circles": [ "\\odot F lieson E D C A" ], "semantics": [ "m \\angle BAC = 38", "m \\angle DEB = m \\angle 2", "m \\widehat DE = 70" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_398.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P" ], "lines": [ "line K E F G A", "line L P O N M", "line B G N H", "line C F O I", "line D E P J" ], "circles": [], "semantics": [ "DJ \\parallel CI \\parallel BH", "EF = 20-5x", "PO = y", "GF = EF = 2x+6", "ON = \\frac{3}{5}y+2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_399.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line A C", "line B C" ], "circles": [], "semantics": [ "BA \\perp AC on A", "BA = 18", "AC = 15", "m \\angle ABC = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_400.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line A C", "line B C" ], "circles": [], "semantics": [ "AC \\perp BC on C", "AB = 18", "CB = x", "m \\angle BAC = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_401.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C E", "line D C A", "line B D", "line A E", "line B A", "line D E" ], "circles": [], "semantics": [ "m \\angle ECD = 63", "m \\angle CAE = 37", "m \\angle CBD = m \\angle 3", "m \\angle CDB = m \\angle 1", "m \\angle CEA = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_402.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "C", "D" ], "lines": [ "line A E C", "line D C", "line D E B", "line A B", "line A D", "line B C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_403.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "N", "P", "M", "R" ], "lines": [ "line N R P", "line R M" ], "circles": [ "\\odot R lieson N P M" ], "semantics": [ "m \\angle NRM = 80" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_404.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "A" ], "lines": [ "line B C", "line C D", "line A D", "line B A", "line B D" ], "circles": [], "semantics": [ "BA = CD", "m \\angle ABD = 4x-1", "m \\angle CDB = x+38" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_405.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "K", "F", "J" ], "lines": [ "line K J F", "line X F", "line X J", "line X K" ], "circles": [], "semantics": [ "m \\angle JKX = m \\angle 1", "m \\angle JFX = m \\angle 2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_406.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "H", "F", "D", "E", "C" ], "lines": [ "line H C E", "line G C D", "line C F" ], "circles": [ "\\odot C lieson H D E F G" ], "semantics": [ "GD \\perp CF on C" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_407.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D", "E" ], "lines": [ "line B C D", "line B A" ], "circles": [ "\\odot E lieson C A D" ], "semantics": [ "BA = 5", "BC = x", "CD = 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_408.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "K", "R", "T", "A", "U" ], "lines": [ "line Q K R", "line P U R", "line P T Q", "line Q A U", "line T A R", "line P A K" ], "circles": [], "semantics": [ "m \\angle QAK = 20", "m \\angle KRA = 40", "m \\angle TPA = 3x+2", "m \\angle UPA = 4x-9" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_409.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line E C D", "line F C B" ], "circles": [ "\\odot A lieson F D B E" ], "semantics": [ "m \\angle ECF = a", "m \\angle DCF = b", "m \\widehat BD = 45", "m \\widehat EF = 145" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_410.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D" ], "lines": [ "line A D", "line C D", "line B C", "line B A" ], "circles": [], "semantics": [ "BC \\perp BA on B", "CD \\perp BC on C", "AD \\perp BA on A", "AD \\perp CD on D", "CD = AD = BC = BA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_411.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "E", "F" ], "lines": [ "line C E B", "line A E D" ], "circles": [ "\\odot F lieson A C D B" ], "semantics": [ "m \\angle CEA = 65", "m \\widehat BD = 72" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_412.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C A", "line C B", "line A B" ], "circles": [], "semantics": [ "CB \\perp AB on B", "AC = 9", "CB = k", "AB = h", "m \\angle ACB = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_413.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "V", "U", "T", "S", "W" ], "lines": [ "line R T", "line S T", "line S R", "line U W", "line V W", "line U V" ], "circles": [], "semantics": [ "m \\angle WUV = m \\angle WVU = m \\angle TSR = m \\angle UWV = m \\angle RTS = m \\angle TRS" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_414.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J" ], "lines": [ "line F A E", "line G E D", "line C D H", "line B C I", "line A B J" ], "circles": [], "semantics": [ "m \\angle BAF = 3x+10", "m \\angle CBJ = 6x-5", "m \\angle GEA = 2x-5", "m \\angle HDE = 5x", "m \\angle DCI = 2x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_415.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B" ], "lines": [ "line A C", "line B C" ], "circles": [ "\\odot C lieson A B" ], "semantics": [ "AC = 10", "m major \\widehat BA = 293" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_416.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "E", "F" ], "lines": [ "line C E D", "line B E A" ], "circles": [ "\\odot F lieson C B D A" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_417.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "F", "K", "N", "M", "H", "L", "J", "A", "B", "C", "D", "E", "I", "O", "P", "Q", "R", "S", "T" ], "lines": [ "line D J L N Q", "line T G K N P", "line S G H J E", "line R K L M I", "line B F J M O", "line C F H K A" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_418.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C A E", "line B A D" ], "circles": [], "semantics": [ "m \\angle BAE = m \\angle 11", "m \\angle DAE = m \\angle 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_419.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "W", "Y", "X" ], "lines": [ "line X Y", "line W X" ], "circles": [ "\\odot X lieson W Y" ], "semantics": [ "XY = 9.4", "m \\angle WXY = 228" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_420.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "H", "F", "G" ], "lines": [ "line E G", "line E H", "line E F", "line H G", "line F G" ], "circles": [], "semantics": [ "HG = FG = 24", "HE = 6x-4", "EF = 4x+7" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_421.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B C E", "line A C D" ], "circles": [ "\\odot F lieson B A E D" ], "semantics": [ "BC = 9", "DC = 4", "EC = x", "AC = x+7" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_422.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C E B", "line C A", "line D C", "line D E A" ], "circles": [], "semantics": [ "m \\angle CAE = 32", "m \\angle DCE = 62", "m \\angle DEB = 125", "m \\angle CDE = m \\angle 3", "m \\angle DEC = m \\angle 1", "m \\angle ACE = m \\angle 2", "m \\angle AEC = m \\angle 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_423.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line B A", "line B C" ], "circles": [], "semantics": [ "CB = 54", "AC = 120", "AB = x", "m \\angle ACB = 64" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_424.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "K", "L", "J", "M" ], "lines": [ "line J M", "line K L", "line K J", "line L M" ], "circles": [], "semantics": [ "KJ = 7x", "LM = 3x+14", "m \\angle KLM = 2z-3", "m \\angle JML = 5z-6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_425.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "L", "K", "M", "A" ], "lines": [ "line L M", "line M", "line K", "line L K", "line L A", "line K A M" ], "circles": [], "semantics": [ "KA = 2", "LA = 3", "AM = 5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_426.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "E", "F", "D", "B", "C" ], "lines": [ "line A D", "line A B", "line B C", "line D C", "line E D", "line F E", "line F A" ], "circles": [], "semantics": [ "FA = AB = FE = BC = ED = DC", "m \\angle DAB = m \\angle DAF = m \\angle ADE = m \\angle ADC = 70", "m \\angle EFA = m \\angle ABC = m \\angle DEF = m \\angle BCD = 110" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_427.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "E", "C", "A", "B" ], "lines": [ "line A B E", "line D E", "line C B", "line A C D" ], "circles": [], "semantics": [ "DE \\parallel CB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_428.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "N", "P", "A", "B" ], "lines": [ "line A B" ], "circles": [ "\\odot A lieson M N P B" ], "semantics": [ "BA = 2", "m major \\widehat PM = 270" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_429.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "S", "T" ], "lines": [ "line R S T" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_430.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B D C", "line A C", "line A D", "line A B" ], "circles": [], "semantics": [ "BC \\perp AD on D", "AD = 13", "CA = 17", "m \\angle ABD = 40" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_PGDPHW_431.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "V", "W", "T", "R", "S", "U", "X" ], "lines": [ "line Q X T", "line W X S", "line V X R", "line X U" ], "circles": [ "\\odot X lieson W Q R S T U V" ], "semantics": [ "QT \\perp VR on X" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_432.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "F", "C", "B", "D", "E", "G", "A", "H", "I", "J", "K" ], "lines": [ "line K D C B A", "line J E C", "line I F C", "line C G H" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_433.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "E", "F" ], "lines": [ "line D F", "line E F", "line D E" ], "circles": [], "semantics": [ "ED = 12", "FE = 8", "m \\angle DFE = 82" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_434.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line F G", "line G C", "line F B", "line E A", "line A D", "line B C", "line B A", "line C D", "line E F" ], "circles": [], "semantics": [ "FG = 5", "EF = 1", "AD = 3", "EA = 4" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_435.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line A B", "line C B" ], "circles": [], "semantics": [ "AB \\perp CB on B", "AC = t", "CB = s", "AB = 5", "m \\angle ACB = 60", "m \\angle CAB = 30" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_436.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "V", "W", "X", "A" ], "lines": [ "line W A X", "line V X" ], "circles": [ "\\odot A lieson W V X" ], "semantics": [ "m \\angle VXA = 14" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_437.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line E G H", "line A C G F", "line D C B" ], "circles": [], "semantics": [ "DB \\parallel EH", "m \\angle ACD = 89", "m \\angle EGF = 5x-24" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_438.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C" ], "lines": [ "line B C", "line A C", "line B A" ], "circles": [], "semantics": [ "AB = 77", "CA = 36", "BC = 85" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_439.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "D", "C", "A", "B", "Q" ], "lines": [ "line E Q", "line Q C", "line D Q A", "line Q B" ], "circles": [ "\\odot Q lieson E A B C D" ], "semantics": [ "m \\widehat DC = 59", "m \\widehat AB = 36" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_440.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "C", "D", "F", "N" ], "lines": [ "line C N", "line D N F" ], "circles": [ "\\odot N lieson D E F C" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_441.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "F", "G", "J", "H" ], "lines": [ "line E J", "line J H", "line G H", "line F E", "line F G" ], "circles": [], "semantics": [ "m \\angle EJH = x+10", "m \\angle EFG = x+20", "m \\angle JEF = x", "m \\angle JHG = x-5", "m \\angle HGF = x+5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_442.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "J", "F", "H", "A" ], "lines": [ "line J H", "line G H", "line J A G", "line F A H", "line F J", "line F G" ], "circles": [], "semantics": [ "GA = 2b+5", "JA = 3b+1", "FA = 4w-7", "HA = 2w+3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_443.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line C B", "line D C", "line D A" ], "circles": [], "semantics": [ "CB \\perp DC on C", "DC \\perp DA on D", "AB \\perp DA on A", "AB \\perp CB on B", "AB = BC = 8" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_444.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "E", "B", "D", "C", "F" ], "lines": [ "line C D B", "line C F E", "line A E B", "line A C", "line A F D" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_445.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B A", "line C A" ], "circles": [ "\\odot A lieson C B" ], "semantics": [ "AC = 3", "m \\angle CAB = 32" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_446.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "D", "B", "M", "A" ], "lines": [ "line D B", "line B M A", "line C A", "line C M", "line D M" ], "circles": [], "semantics": [ "BA \\perp CM on M", "DB \\perp BA on B", "DB = CM" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_447.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "J", "K", "M", "N", "L", "Q" ], "lines": [ "line K L", "line J K", "line J L", "line M Q", "line M N", "line Q N" ], "circles": [], "semantics": [ "KL = MQ", "m \\angle LKJ = m \\angle MQN" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_448.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "Z", "Y" ], "lines": [ "line X Y", "line Z Y", "line X Z" ], "circles": [], "semantics": [ "ZY \\perp XZ on Z", "ZX = 2", "YZ = 3", "XY = \\sqrt{13}" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_449.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "P", "B", "E", "F", "G", "H" ], "lines": [ "line F D P C H", "line E A P B G" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_450.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line C B", "line A B" ], "circles": [], "semantics": [ "AB = 9x-1", "AC = 4x+1", "CB = AC = 5x-0.5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_451.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C", "line A B", "line A C" ], "circles": [], "semantics": [ "AC = BC", "m \\angle BCA = 62", "m \\angle CBA = m \\angle BAC" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_452.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C A", "line B A", "line C B" ], "circles": [], "semantics": [ "BA \\perp CB on B", "AB = 26", "CA = x", "m \\angle ACB = 43" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_453.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "F", "D", "E", "A" ], "lines": [ "line G A E", "line G F", "line D E", "line D A F", "line F E", "line G D" ], "circles": [], "semantics": [ "GA = 26", "FA = 19", "DA = x-2", "EA = y+1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_454.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C" ], "lines": [ "line A D", "line D C", "line B C", "line A B" ], "circles": [], "semantics": [ "BA = 9x-11", "DC = 6x+1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_455.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line C D", "line D E", "line B E", "line C B", "line C A E", "line B A D" ], "circles": [], "semantics": [ "CE \\perp BD on A", "CA = AB = AE = DA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_456.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "O" ], "lines": [ "line B O A", "line B C" ], "circles": [ "\\odot O lieson B C A" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_457.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D A", "line C B", "line C D", "line B A" ], "circles": [], "semantics": [ "CD = x+2", "AB = 5x-8", "m \\angle ADC = 62", "m \\angle BCD = m \\angle 2", "m \\angle CBA = m \\angle 3", "m \\angle DAB = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_458.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line D B F", "line C B E" ], "circles": [ "\\odot A lieson C D E F" ], "semantics": [ "CB = 6.5", "DB = 3", "EB = m", "FB = 7" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_459.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I" ], "lines": [ "line B H G E", "line A I G F", "line C H I D" ], "circles": [], "semantics": [ "AF \\perp CD on I", "m \\angle IHG = 38", "m \\angle FGE = 52", "m \\angle FGH = m \\angle 2", "m \\angle IHB = m \\angle 1", "m \\angle IGH = m \\angle 4", "m \\angle HIA = m \\angle 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_460.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "F", "E", "C", "P", "B" ], "lines": [ "line E P C", "line A F C", "line B C", "line A E B", "line F P B" ], "circles": [], "semantics": [ "EA = EB" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_461.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line B D A", "line D C" ], "circles": [ "\\odot D lieson B C A" ], "semantics": [ "m \\angle CBD = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_462.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "E", "F", "A", "C", "D" ], "lines": [ "line A D C", "line A E B", "line B F C", "line D F", "line E D" ], "circles": [], "semantics": [ "ED = 2.3", "AE = EB = 2.5", "m \\angle EBF = 95" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_463.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "P", "S", "R", "Q", "A" ], "lines": [ "line S A Q", "line P A R", "line S R", "line Q R", "line P S", "line P Q" ], "circles": [ "\\odot A lieson P Q R S" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_464.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B C E", "line A D E" ], "circles": [ "\\odot F lieson B C D A" ], "semantics": [ "EC = x", "ED = 8", "BC = 15", "AD = 12" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_465.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "Q", "R", "T", "S", "A" ], "lines": [ "line Q A", "line R A T", "line A S" ], "circles": [ "\\odot A lieson Q R S T" ], "semantics": [ "m \\angle SAR = 130", "m \\angle QAT = 112" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_466.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line B A", "line C D", "line A D", "line B C" ], "circles": [], "semantics": [ "m \\angle ACB = 6x^{2}-3x", "m \\angle CAB = 7x^{2}-10" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_467.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "A", "D" ], "lines": [ "line B C", "line E D C", "line A E", "line A B", "line B E", "line B D" ], "circles": [], "semantics": [ "AE \\perp AB on A", "EC \\perp BD on D", "BC = 5y-22", "BE = 3y", "BD = AB", "m \\angle AEB = 7x-2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_468.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A C B", "line F B", "line D E F", "line D A", "line E C" ], "circles": [], "semantics": [ "AB \\perp EC on C", "AB = b", "CE = h" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_469.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "S", "T", "V", "U" ], "lines": [ "line V T", "line V U", "line S T", "line S V", "line T U" ], "circles": [], "semantics": [ "SV = 3.2", "VU = 4.5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_470.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C E", "line D C B" ], "circles": [], "semantics": [ "m \\angle ACB = m \\angle 2", "m \\angle ECD = m \\angle 1" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_471.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line B C", "line E D", "line E B A", "line D C A" ], "circles": [], "semantics": [ "EB = 7y", "DC = 12-2x", "AB = 5y+16", "AC = DC = 8x-18", "m \\angle DEB = m \\angle CBA" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_472.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "C", "B", "D" ], "lines": [ "line C D", "line B D", "line C B" ], "circles": [], "semantics": [ "CD = 18", "CB = 11", "BD = 15" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_473.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "K", "F", "H", "L", "G" ], "lines": [ "line F H", "line F G L", "line K L", "line K G H" ], "circles": [], "semantics": [ "FH \\parallel KL", "GL = FG" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_474.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "H", "M", "J", "L", "K" ], "lines": [ "line L K", "line M L", "line H J", "line G M", "line J K", "line G H" ], "circles": [], "semantics": [ "GH = GM = HJ = LM = JK = KL" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_475.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "W", "X", "Y", "Z", "A" ], "lines": [ "line Z Y", "line X A Z", "line W X", "line W A Y" ], "circles": [ "\\odot A lieson W X Y Z" ], "semantics": [ "m \\angle XWA = m \\angle 1", "m \\angle AXW = m \\angle 2", "m \\angle XAW = m \\angle 3", "m \\angle ZAY = m \\angle 4", "m \\angle YZA = m \\angle 6", "m \\angle ZYA = m \\angle 5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_476.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line B C", "line A C" ], "circles": [], "semantics": [ "AB \\perp BC on B", "CA = x", "AB = 17", "BC = 7" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_477.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K" ], "lines": [ "line A I H", "line H J G", "line G F E", "line B D E", "line A C B" ], "circles": [ "\\odot K lieson C I J F D" ], "semantics": [ "AI = GF = 5", "ED = 7", "AB = 11", "GH = 7.5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_478.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C B", "line D C" ], "circles": [], "semantics": [ "m \\angle ACD = 4n+5", "m \\angle BCD = 8n-5" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_479.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D E A", "line B E C", "line D B", "line D C", "line C A", "line B A" ], "circles": [], "semantics": [ "BC \\perp DA on E", "BE = AE", "m \\angle EDC = m \\angle 2", "m \\angle EDB = m \\angle 1", "m \\angle ECA = m \\angle 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_480.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "A", "C", "D", "B" ], "lines": [ "line A E", "line E B D", "line A B C", "line D C" ], "circles": [], "semantics": [ "DC \\parallel AE", "AB = x+3", "EB = 5", "CB = 2x-8", "DB = 3" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_481.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C B", "line A B" ], "circles": [], "semantics": [ "CB \\perp AB on B", "CB = BA = 3\\frac{1}{2}" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_482.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line C D", "line D B A", "line A E", "line C B E" ], "circles": [ "\\odot F lieson C D E A" ], "semantics": [ "CD \\parallel AE", "m \\angle AEB = c", "m \\angle ABE = d", "m \\angle BAE = b", "m \\angle BDC = 40", "m \\widehat AC = a" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_483.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B" ], "lines": [ "line D C", "line C B", "line A B", "line D A", "line D B" ], "circles": [], "semantics": [ "DA \\parallel CB", "AB \\perp DA on A", "DC \\perp CB on C", "BA = 18", "m \\angle ADB = 68" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_484.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D" ], "lines": [ "line B A", "line B C", "line C D", "line A D" ], "circles": [], "semantics": [ "m \\angle ABC = m \\angle DCB = 2x", "m \\angle CDA = m \\angle BAD = x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_PGDPHW_485.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "Y", "Z", "W", "U", "V" ], "lines": [ "line Y U Z", "line X W Z", "line Y X", "line Y V W", "line X V U" ], "circles": [], "semantics": [ "YZ \\perp YX on Y", "XZ \\perp YW on W", "YU = UZ" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_486.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line A D", "line C B", "line D C" ], "circles": [], "semantics": [ "AD = 1.7", "BA = 2.1", "DC = 0.9", "m \\angle BAD = 45" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_487.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "G", "H", "N", "J", "P", "M", "A", "B", "C" ], "lines": [ "line G A B P", "line G M J", "line H P J", "line G N H", "line N A C J", "line H B C M" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_488.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "E", "D", "F" ], "lines": [ "line B D A", "line B E C", "line D F C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_489.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line C D", "line H F G", "line E G", "line D E", "line B H", "line A F", "line C B" ], "circles": [], "semantics": [ "AF = 6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_490.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "M", "J", "L", "Q", "K", "N" ], "lines": [ "line M J L", "line N K L" ], "circles": [ "\\odot Q lieson M J K N" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_491.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "E", "F", "G", "J", "H" ], "lines": [ "line J G F", "line J H", "line E G H", "line E F" ], "circles": [], "semantics": [ "EF \\parallel JH", "JG = 20", "HG = 15", "FG = x+9", "EG = 2x-2" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_492.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "T", "Q", "S", "R", "P", "A", "B" ], "lines": [ "line Q B R", "line T A S", "line B P", "line P A" ], "circles": [ "\\odot P lieson Q R S T" ], "semantics": [ "QR \\perp BP on B", "TS \\perp PA on A", "QR = 7x-20", "BP = PA = 9", "TS = 3x" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_493.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B", "E", "F", "G", "H", "I", "J", "K", "L", "M" ], "lines": [ "line A H B", "line D K E L B", "line A I E J C", "line C G B", "line D F A", "line D M C" ], "circles": [ "\\odot E lieson F K M J G L H I" ], "semantics": [] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_494.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line D C", "line A C", "line D B", "line B A", "line B C" ], "circles": [], "semantics": [ "BC = 11", "DA = 25" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_495.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line E D B A", "line F G C A" ], "circles": [ "\\odot H lieson D B C G" ], "semantics": [ "m \\angle BAC = x", "m \\widehat CB = 45", "m \\widehat GD = 125" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_496.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "R", "S", "Q", "A", "B", "C", "D", "E", "F" ], "lines": [ "line B R S A", "line C R Q D", "line E S F" ], "circles": [], "semantics": [ "CD \\parallel EF", "m \\angle BRQ = x", "m \\angle RSF = 118" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_497.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "K", "A", "N", "O", "L" ], "lines": [ "line N O", "line L N", "line K L", "line A K", "line A N", "line A L", "line L O", "line K O" ], "circles": [], "semantics": [ "AN = OK = 8.5", "KA = 4.7", "AL = LO = 4", "ON = 6.5", "LK = NL = 6" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_498.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "X", "W", "Z", "Y", "T" ], "lines": [ "line Z Y", "line X Y", "line W X", "line X T Z", "line W Z", "line W T Y" ], "circles": [], "semantics": [ "WX \\parallel ZY", "XY = WZ" ] }, { "diagram": "PGDP/handwritten/image/PGDPHW_test_PGDPHW_499.png", "style": "handwritten", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "Q" ], "lines": [ "line B Q D", "line A Q C" ], "circles": [ "\\odot Q lieson B C D A" ], "semantics": [ "m \\angle DQC = 47" ] }, { "diagram": "PGDP/printed/image/WeMath_124_990.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "D", "A", "C", "B" ], "lines": [ "line A B", "line D H C", "line A C", "line A H", "line A D", "line B C" ], "circles": [], "semantics": [ "AB = 5", "AH = 2", "AD = 2.5" ] }, { "diagram": "PGDP/printed/image/WeMath_460_3673.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "A" ], "lines": [ "line A C", "line A D", "line A B", "line B D C" ], "circles": [], "semantics": [ "AB = AC = 3", "m \\angle ABC = 60°", "AD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/WeMath_106_841.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "O", "B", "A" ], "lines": [ "line A B", "line O D", "line A O C", "line D C", "line O B", "line C B", "line A D" ], "circles": [ "\\odot O lieson A B C D" ], "semantics": [ "m \\angle OCD = 60", "m \\angle BCO = 75" ] }, { "diagram": "PGDP/printed/image/WeMath_456_3641.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "E", "B" ], "lines": [ "line A B C D E" ], "circles": [], "semantics": [ "AB = BC = CD = DE", "AC = 4" ] }, { "diagram": "PGDP/printed/image/WeMath_101_801.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "A", "Z", "B", "H", "O" ], "lines": [ "line O H B", "line O M", "line M H", "line A M B", "line A O" ], "circles": [], "semantics": [ "m \\angle AOM = m \\angle BOM", "MH = 2", "AO = 5" ] }, { "diagram": "PGDP/printed/image/WeMath_106_848.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "O", "A" ], "lines": [ "line A B", "line A O C", "line O B", "line C B" ], "circles": [ "\\odot O lieson A B C" ], "semantics": [ "m \\angle OCB = 75" ] }, { "diagram": "PGDP/printed/image/WeMath_349_2786.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A" ], "lines": [ "line B A", "line C A", "line C B" ], "circles": [], "semantics": [ "BA \\perp CB on B" ] }, { "diagram": "PGDP/printed/image/WeMath_133_1059.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "M", "C", "E" ], "lines": [ "line B C", "line D M B", "line A B", "line D C", "line A M C", "line A D" ], "circles": [], "semantics": [ "MA = 1.26", "BD = 3.97" ] }, { "diagram": "PGDP/printed/image/WeMath_126_1002.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "B" ], "lines": [ "line B C", "line D B", "line A B", "line D C", "line A D" ], "circles": [], "semantics": [ "AB = 4.5", "AD = 4" ] }, { "diagram": "PGDP/printed/image/WeMath_2864.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "D", "C", "M", "N", "A", "O" ], "lines": [ "line A E", "line A N C", "line A D", "line E N O B", "line D M O C", "line A M B" ], "circles": [], "semantics": [ "AD = 1", "AE = 1", "AB = AC" ] }, { "diagram": "PGDP/printed/image/WeMath_2521.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "D", "A", "C", "F" ], "lines": [ "line A F D", "line B E C", "line D C", "line F E", "line A B" ], "circles": [], "semantics": [ "CD = 2.35", "EF = 3.14", "AB = 3.69", "CD \\parallel BA" ] }, { "diagram": "PGDP/printed/image/WeMath_2370.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "O", "E", "C" ], "lines": [ "line A O", "line A C B", "line E O C D", "line A D", "line E A", "line O B", "line D B" ], "circles": [ "\\odot O lieson E B D A" ], "semantics": [ "AB \\perp ED on C", "OE = 4", "m \\angle OEA = 30" ] }, { "diagram": "PGDP/printed/image/WeMath_2297.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "F", "O", "C", "A" ], "lines": [ "line A F C", "line B O F", "line A O E", "line B E C", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/WeMath_2444.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "D", "A", "C", "B" ], "lines": [ "line B C", "line A M B", "line D C", "line M C", "line A C", "line A D" ], "circles": [], "semantics": [ "AB \\perp MC on M" ] }, { "diagram": "PGDP/printed/image/WeMath_5786.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "F", "E", "C", "B" ], "lines": [ "line C D", "line B C", "line A F", "line D E", "line F D", "line B A", "line F E", "line B F" ], "circles": [], "semantics": [ "AB = 3" ] }, { "diagram": "PGDP/printed/image/WeMath_2412.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "O", "D" ], "lines": [ "line D C", "line D O B", "line A D", "line B C", "line A O C", "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/WeMath_2582.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "O", "B" ], "lines": [ "line C A", "line B A", "line D O", "line O A", "line B O C" ], "circles": [ "\\odot O lieson B A C D" ], "semantics": [ "AC = 4", "m \\angle AOC = 60" ] }, { "diagram": "PGDP/printed/image/WeMath_1072.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "O", "A" ], "lines": [ "line B O", "line O A" ], "circles": [ "\\odot O lieson A B" ], "semantics": [ "AO = 12", "m \\angle BOA = \\theta = 120" ] }, { "diagram": "PGDP/printed/image/WeMath_5436.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line B C A" ], "circles": [ "\\odot A lieson C", "\\odot B lieson C" ], "semantics": [] }, { "diagram": "PGDP/printed/image/WeMath_1064.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "O" ], "lines": [ "line O A", "line O B" ], "circles": [ "\\odot O lieson A B" ], "semantics": [ "OA = 8", "m \\angle AOB = \\theta = \\frac{\\pi}{6}" ] }, { "diagram": "PGDP/printed/image/WeMath_2561.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "G", "F", "D" ], "lines": [ "line D C", "line A F D", "line G D", "line B E C", "line A B", "line D E", "line F G B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/WeMath_1075.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "B" ], "lines": [ "line O A", "line O B" ], "circles": [ "\\odot O lieson A B" ], "semantics": [ "OA = 6", "m \\angle BOA = \\theta = 30" ] }, { "diagram": "PGDP/printed/image/WeMath_2659.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "D", "B", "C", "F", "A" ], "lines": [ "line A D C", "line E F D", "line A F B", "line E B C", "line D B", "line A E" ], "circles": [ "\\odot G lieson A D B E" ], "semantics": [ "BD = 4", "AD = 4", "m \\angle FAE = 68" ] }, { "diagram": "PGDP/printed/image/WeMath_2272.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A B", "line B C", "line A C" ], "circles": [], "semantics": [ "AB = 3", "m \\angle ABC = m \\angle ACB" ] }, { "diagram": "PGDP/printed/image/WeMath_2225.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "A", "D", "C", "B" ], "lines": [ "line A H D C", "line B H", "line B D", "line B C", "line A B" ], "circles": [], "semantics": [ "m \\angle BAC = 2 \\angle BCA", "BC \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/WeMath_352.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "C" ], "lines": [ "line B C", "line A B", "line D C", "line A D" ], "circles": [], "semantics": [ "CD = \\frac{4}{5}" ] }, { "diagram": "PGDP/printed/image/WeMath_942.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "A", "E", "B" ], "lines": [ "line C A", "line C D", "line E D A B" ], "circles": [ "\\odot A lieson E C B" ], "semantics": [] }, { "diagram": "PGDP/printed/image/WeMath_2822.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "G", "A", "C", "F", "E" ], "lines": [ "line E F G", "line B D G C", "line A D", "line E A B", "line A F C" ], "circles": [], "semantics": [ "BC \\perp AD on D", "EG \\perp BC on G", "DG = 1", "AD = 2", "BD = 1", "m \\angle DAF = 45.11", "m \\angle EFA = 45.11" ] }, { "diagram": "PGDP/printed/image/WeMath_2475.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "P", "B" ], "lines": [ "line B C", "line D P B", "line A B", "line D C", "line A D" ], "circles": [], "semantics": [ "BD = 6" ] }, { "diagram": "PGDP/printed/image/WeMath_2506.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "O", "B" ], "lines": [ "line A B", "line O A", "line C B", "line O C" ], "circles": [], "semantics": [ "OA = 4", "AB = 8" ] }, { "diagram": "PGDP/printed/image/WeMath_1078.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "B" ], "lines": [ "line B O", "line O A" ], "circles": [ "\\odot O lieson B A" ], "semantics": [ "BO \\perp OA on O", "AO = 5", "m \\angle AOB = \\theta = \\frac{\\pi}{2}" ] }, { "diagram": "PGDP/printed/image/WeMath_2480.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "M", "C", "O", "N" ], "lines": [ "line B C", "line N O M", "line A N B", "line A D", "line D M C", "line B O D", "line A O C" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/WeMath_2479.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "O", "B" ], "lines": [ "line B C", "line A B", "line A D", "line D C", "line B O D", "line A O C" ], "circles": [], "semantics": [ "AB = CD" ] }, { "diagram": "PGDP/printed/image/WeMath_2342.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "E", "F", "A", "O" ], "lines": [ "line A F C", "line A O D", "line B O F", "line B D C", "line A E B", "line E O C" ], "circles": [], "semantics": [ "BE = AE", "AF = CF", "BD = CD" ] }, { "diagram": "PGDP/printed/image/WeMath_2227.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "H" ], "lines": [ "line A H D C", "line B H", "line B D", "line B C", "line A B" ], "circles": [], "semantics": [ "AC \\perp BH on H", "BH = HD" ] }, { "diagram": "PGDP/printed/image/WeMath_2532.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "M", "D", "A", "N", "C" ], "lines": [ "line B C", "line B N", "line A B", "line D M N C", "line A M", "line A D" ], "circles": [], "semantics": [ "AM \\perp CD on M", "BN \\perp CD on N", "AM = MN = 3" ] }, { "diagram": "PGDP/printed/image/WeMath_2676.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "O", "E", "C" ], "lines": [ "line A O", "line A C B", "line E O C D", "line A D", "line E A", "line O B", "line D B" ], "circles": [ "\\odot O lieson E B D A" ], "semantics": [ "AB \\perp ED on C", "EO = 4", "m \\angle OEA = 30" ] }, { "diagram": "PGDP/printed/image/WeMath_2288.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "E", "B", "F", "C", "K", "A" ], "lines": [ "line A C", "line A K", "line A F", "line A E", "line B K M E F C", "line A B", "line A M" ], "circles": [], "semantics": [ "m \\angle AEB = 90" ] }, { "diagram": "PGDP/printed/image/WeMath_2380.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "D", "A", "O" ], "lines": [ "line A D", "line D O B", "line D C", "line A O C", "line B C", "line A B" ], "circles": [], "semantics": [ "BD = 3" ] }, { "diagram": "PGDP/printed/image/WeMath_5146.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "B" ], "lines": [ "line B C", "line A B", "line D C", "line A D" ], "circles": [], "semantics": [ "AB = 3", "CD = 3" ] }, { "diagram": "PGDP/printed/image/WeMath_2400.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "O" ], "lines": [ "line A B", "line O A", "line C B", "line O C" ], "circles": [], "semantics": [ "OA = 4", "AB = 6" ] }, { "diagram": "PGDP/printed/image/WeMath_2348.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A B", "line A D", "line B D", "line C D", "line B C", "line A C" ], "circles": [], "semantics": [ "m \\angle ABD = 24.9" ] }, { "diagram": "PGDP/printed/image/WeMath_2216.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "B", "C" ], "lines": [ "line A O B", "line C O" ], "circles": [], "semantics": [ "m \\angle BOC = 45" ] }, { "diagram": "PGDP/printed/image/WeMath_3000.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A" ], "lines": [ "line A B", "line A C", "line C B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/WeMath_2484.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "D", "A", "C", "O", "E", "N", "B" ], "lines": [ "line D O B", "line N O M", "line A N B", "line D M C", "line A O C", "line A D", "line B C" ], "circles": [], "semantics": [ "AC = 3.87", "BD = 5.6" ] }, { "diagram": "PGDP/printed/image/WeMath_2345.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "H" ], "lines": [ "line A F C", "line F H B", "line A H D", "line B D C", "line E H C", "line A E B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/WeMath_2113.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B" ], "lines": [ "line A B" ], "circles": [], "semantics": [] }, { "diagram": "PGDP/printed/image/WeMath_2543.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "M", "D", "A", "C" ], "lines": [ "line B C", "line A B", "line D M C", "line A M", "line A D" ], "circles": [], "semantics": [ "AM \\perp CD on M", "AB = 2", "CD = 4", "m angle MAD = 30" ] }, { "diagram": "PGDP/printed/image/WeMath_2488.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "C" ], "lines": [ "line B C", "line A B", "line D C", "line A D" ], "circles": [], "semantics": [ "AD = 4" ] }, { "diagram": "PGDP/printed/image/WeMath_2918.jpg", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "F", "B'", "D", "C", "E", "N", "A" ], "lines": [ "line A D N C", "line B' M", "line F N", "line E M F", "line B' F C", "line D F", "line A E B'" ], "circles": [], "semantics": [ "CF = 4.5", "BF = 1.5", "BM = 1.19", "m \\angle EBF = 75", "m \\angle DFC = 75" ] }, { "diagram": "PGDP/printed/image/MathVR_50346_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "C", "D", "I" ], "lines": [ "line D I E", "line A E C", "line A D B", "line B I", "line B C", "line A I", "line I C" ], "circles": [], "semantics": [ "DE \\perp AI on I" ] }, { "diagram": "PGDP/printed/image/MathVR_17034_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "D" ], "lines": [ "line D B", "line A E", "line A D", "line A B C", "line B E" ], "circles": [], "semantics": [ "m \\angle CBE = m \\angle 2", "m \\angle ABE = m \\angle 4", "m \\angle DBA = m \\angle 3", "m \\angle DBC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_71055_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "O" ], "lines": [ "line E D", "line C D B", "line A F E C", "line F O", "line O D", "line A O B" ], "circles": [ "\\odot O lieson F D B" ], "semantics": [ "ED \\perp AC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_56108_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "F", "B", "E", "C", "G", "A" ], "lines": [ "line D C", "line A D", "line B F C", "line D G F", "line E G C", "line A E B" ], "circles": [], "semantics": [ "EC \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_52190_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "C", "D", "F", "B" ], "lines": [ "line B C", "line A D F B", "line E F", "line E D", "line A C" ], "circles": [], "semantics": [ "AB \\perp ED on D", "BC \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_23024_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "H", "G", "D", "A", "E", "F" ], "lines": [ "line F G", "line E H B", "line E D C", "line E F", "line B C G", "line A B", "line A D", "line H D G" ], "circles": [], "semantics": [ "EC \\perp BG on C" ] }, { "diagram": "PGDP/printed/image/MathVR_23938_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "H", "C", "I", "F", "E", "A", "G" ], "lines": [ "line I G D", "line A E C", "line H F E", "line B D C", "line F G", "line A H I B", "line E D" ], "circles": [], "semantics": [ "ID \\perp AB on I", "HE \\perp AB on H" ] }, { "diagram": "PGDP/printed/image/MathVR_41527_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "C", "E", "M", "H", "D", "I", "B", "F", "A" ], "lines": [ "line H M E", "line A I D", "line G F", "line E F", "line H I G", "line B C", "line D E C", "line M D", "line A B" ], "circles": [], "semantics": [ "HE \\perp MD on M" ] }, { "diagram": "PGDP/printed/image/MathVR_46178_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "A", "M", "O", "B", "E", "C" ], "lines": [ "line B C", "line N E C O M", "line A B O", "line A E" ], "circles": [], "semantics": [ "NM \\perp AE on E", "BC \\perp NM on C", "m \\angle COB = 30" ] }, { "diagram": "PGDP/printed/image/MathVR_44156_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "O", "B", "A", "C", "D", "E" ], "lines": [ "line A D", "line D E", "line D O B", "line B F C E", "line D C", "line A O C", "line A B", "line D F" ], "circles": [], "semantics": [ "BE \\perp DF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_9527_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "B", "A", "E", "C", "P", "D" ], "lines": [ "line D C", "line B F D", "line A D", "line P F", "line B C", "line A E C", "line P E", "line A P B" ], "circles": [], "semantics": [ "BD \\perp PF on F", "AC \\perp PE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_63379_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C" ], "lines": [ "line A C", "line B C", "line A B" ], "circles": [], "semantics": [ "CA = 50", "BA = 30", "m \\angle CAB = 150" ] }, { "diagram": "PGDP/printed/image/MathVR_75244_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "E", "A", "C" ], "lines": [ "line D C", "line A B", "line D E", "line A D", "line E B", "line A E C", "line C B" ], "circles": [], "semantics": [ "m \\angle ECB = m \\angle 2", "m \\angle DAE = m \\angle 3", "m \\angle DCE = m \\angle 1", "m \\angle BAE = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/MathVR_22514_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "O" ], "lines": [ "line A C", "line B O", "line B C", "line A B", "line O C" ], "circles": [], "semantics": [ "m \\angle ACO = m \\angle 3", "m \\angle BCO = m \\angle 4", "m \\angle OBC = m \\angle 1", "m \\angle OBA = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_72489_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "G", "B", "C", "O" ], "lines": [ "line B D", "line A C", "line A G O D", "line B G", "line B A", "line B O C", "line G C", "line D C" ], "circles": [], "semantics": [ "m \\angle DEB = m \\angle o" ] }, { "diagram": "PGDP/printed/image/MathVR_5950_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "E", "O", "A", "B" ], "lines": [ "line C E D", "line A O E B" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [ "CD \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_71263_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "C", "P", "A", "D" ], "lines": [ "line A P", "line D P C", "line A D", "line B P", "line B C", "line A E B", "line E P" ], "circles": [], "semantics": [ "AB \\perp EP on E" ] }, { "diagram": "PGDP/printed/image/MathVR_51461_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "B", "A", "C", "F" ], "lines": [ "line B F", "line D C", "line A D", "line A F", "line B E C", "line D F E", "line A B" ], "circles": [], "semantics": [ "AD \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_17719_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "M", "C", "N", "O", "B", "F", "E" ], "lines": [ "line C F", "line E F M N", "line A C E", "line A O B M", "line C B N", "line C O" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "m \\angle MBN = m \\angle 1", "m \\angle BCO = m \\angle 2", "m \\angle OBC = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_5616_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B" ], "lines": [ "line D B", "line C B", "line D C A", "line B A" ], "circles": [], "semantics": [ "DB \\perp DA on D", "m \\angle CAB = 30", "m \\angle BCD = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_37172_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "F", "E", "O", "C" ], "lines": [ "line C B", "line A F O E C", "line D C", "line D F", "line A B", "line E B", "line D O B", "line D A" ], "circles": [], "semantics": [ "AC \\perp DF on F", "AC \\perp EB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_75376_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "A", "B", "C", "D", "E" ], "lines": [ "line B D C", "line A E D", "line E F", "line B E", "line A F C", "line B A", "line E C" ], "circles": [], "semantics": [ "EF \\perp AC on F" ] }, { "diagram": "PGDP/printed/image/MathVR_31718_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "A", "E", "F", "B", "P", "C" ], "lines": [ "line C E B", "line A P E", "line C P H", "line A H B", "line C F A", "line F P B" ], "circles": [], "semantics": [ "CH \\perp AB on H" ] }, { "diagram": "PGDP/printed/image/MathVR_73439_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "C", "O", "D", "A", "E" ], "lines": [ "line A F D", "line D C", "line B O D", "line F O E", "line B E C", "line A O C", "line A B" ], "circles": [], "semantics": [ "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_21408_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "A", "O", "F", "B", "P", "C" ], "lines": [ "line A P", "line A O F E", "line A C", "line B A", "line B F D C P", "line A D" ], "circles": [ "\\odot O lieson A C E B" ], "semantics": [ "BP \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_74444_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "E" ], "lines": [ "line C D", "line E D A", "line B C E", "line B A" ], "circles": [], "semantics": [ "CD \\perp BE on C", "EA \\perp BA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_74440_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "M", "F", "E", "A", "B", "G" ], "lines": [ "line A F M", "line M G C", "line A E G D", "line C D", "line B A", "line B F E C" ], "circles": [], "semantics": [ "m \\angle MFB = m \\angle 5", "m \\angle FAE = m \\angle 2", "m \\angle FAB = m \\angle 1", "m \\angle GCD = m \\angle 4", "m \\angle GCE = m \\angle 3", "m \\angle MGD = m \\angle 6" ] }, { "diagram": "PGDP/printed/image/MathVR_79380_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "G", "M", "C", "H", "D", "F" ], "lines": [ "line A M D", "line F D C", "line M H G", "line E G", "line B G C", "line E M F", "line A E B", "line F G" ], "circles": [], "semantics": [ "MG \\perp EF on M" ] }, { "diagram": "PGDP/printed/image/MathVR_2045_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "F", "D" ], "lines": [ "line F E", "line D E C", "line A F D", "line B E", "line B C", "line A B", "line F B" ], "circles": [], "semantics": [ "m \\angle AFB = m \\angle 3", "m \\angle EBC = m \\angle 5", "m \\angle FEB = m \\angle 6", "m \\angle ABF = m \\angle 2", "m \\angle EFD = m \\angle 1", "m \\angle EBF = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/MathVR_52611_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "E", "B", "H", "P", "C", "F", "O" ], "lines": [ "line A O P B", "line F B", "line A H D F", "line H O", "line D P", "line D O", "line E C A", "line E D" ], "circles": [ "\\odot O lieson A C D B" ], "semantics": [ "m \\angle HAC = m \\angle 1", "m \\angle HDO = m \\angle 3", "m \\angle OAH = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_64822_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D", "E" ], "lines": [ "line A E", "line E D", "line B E C", "line A B", "line D C" ], "circles": [], "semantics": [ "m \\angle EAB = m \\angle 1", "m \\angle EDC = m \\angle 4", "m \\angle AEB = m \\angle 2", "m \\angle DEC = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_70853_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "A", "P", "F", "D", "B" ], "lines": [ "line P D C", "line C B", "line A C", "line A E F B", "line C F", "line D E", "line D A" ], "circles": [], "semantics": [ "AB \\perp DE on E", "AB \\perp CF on F", "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_4272_image2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "B", "C", "A", "F", "D", "E" ], "lines": [ "line C D", "line A D B", "line C G B F", "line D G", "line A E C", "line E D F" ], "circles": [], "semantics": [ "m \\angle ADE = m \\angle 2", "m \\angle BDF = m \\angle 1", "m \\angle CDG = m \\angle 3", "m \\angle DCG = m \\angle 4", "m \\angle GDB = m \\angle 5" ] }, { "diagram": "PGDP/printed/image/MathVR_22241_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D" ], "lines": [ "line B C", "line A B", "line B D", "line A D", "line A C" ], "circles": [], "semantics": [ "BC \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_66352_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "M", "A" ], "lines": [ "line D C", "line A D", "line B C", "line M D", "line B M A" ], "circles": [], "semantics": [ "DC \\perp MD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_32093_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B", "O" ], "lines": [ "line D B", "line A B", "line C B", "line A D C" ], "circles": [ "\\odot O lieson C B A" ], "semantics": [ "DB \\perp AC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_9484_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "E", "D", "F" ], "lines": [ "line C B", "line E F", "line C E", "line A C", "line B F", "line A E B D", "line F D" ], "circles": [], "semantics": [ "CB \\perp AC on C", "EF \\perp DF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_4456_image2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "A", "O", "C", "F", "B" ], "lines": [ "line F D", "line D B", "line A D", "line E D C", "line A O B C", "line A F E", "line O D" ], "circles": [ "\\odot O lieson A B D F" ], "semantics": [ "m \\angle DAF = m \\angle 4", "m \\angle DBO = m \\angle 5", "m \\angle DFA = m \\angle 1", "m \\angle OAD = m \\angle 3", "m \\angle ODA = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_9331_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "Q", "A", "D", "B", "H", "C" ], "lines": [ "line Q B", "line C B", "line A Q C", "line D C", "line D Q P", "line A P B", "line D H A", "line H Q" ], "circles": [], "semantics": [ "DA \\perp HQ on H" ] }, { "diagram": "PGDP/printed/image/MathVR_67686_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "G", "B", "A", "C", "E", "F" ], "lines": [ "line D F", "line E G", "line A D", "line A E", "line A G", "line B G C", "line D C", "line D E", "line A B", "line C F" ], "circles": [], "semantics": [ "DF \\perp DE on D" ] }, { "diagram": "PGDP/printed/image/MathVR_54080_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "C", "B", "A", "D", "E" ], "lines": [ "line E D", "line D O", "line E O", "line C O A", "line B D A", "line B E C" ], "circles": [ "\\odot O lieson C D A" ], "semantics": [ "m \\angle DOE = m \\angle 2", "m \\angle EOC = m \\angle 1", "m \\angle ODA = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_65947_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "M", "F", "D", "A" ], "lines": [ "line M C", "line D F C", "line A D", "line E F", "line B C", "line A E M B" ], "circles": [], "semantics": [ "MC \\perp AB on M" ] }, { "diagram": "PGDP/printed/image/MathVR_5392_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "O", "P" ], "lines": [ "line O P A", "line C P B", "line B A", "line l lieson A C" ], "circles": [ "\\odot O lieson B P" ], "semantics": [ "OA \\perp line l on A" ] }, { "diagram": "PGDP/printed/image/MathVR_47691_img4.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A E C", "line B D C", "line A H G B", "line F B", "line F G D", "line E D", "line A D", "line F H E" ], "circles": [], "semantics": [ "AD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_63626_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "C", "A", "B", "D" ], "lines": [ "line E D", "line C B", "line A D B", "line A E C" ], "circles": [], "semantics": [ "ED \\perp AB on D", "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_75705_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "B", "G", "C", "E", "D", "A" ], "lines": [ "line A D C", "line A E B", "line E G D", "line B D", "line B F C", "line G F", "line E C" ], "circles": [], "semantics": [ "AB \\perp EC on E", "AC \\perp BD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_9426_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "E", "C", "P", "A" ], "lines": [ "line D C", "line E P D", "line A P B", "line A D", "line E B C", "line P C" ], "circles": [], "semantics": [ "AB \\perp EC on B" ] }, { "diagram": "PGDP/printed/image/MathVR_6913_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "D", "M", "O", "C" ], "lines": [ "line A C M", "line D M", "line B E A", "line B D", "line A D", "line E D", "line B C", "line D C" ], "circles": [ "\\odot O lieson A C D B" ], "semantics": [ "BA \\perp ED on E" ] }, { "diagram": "PGDP/printed/image/MathVR_62288_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "P", "A'", "C", "D", "A" ], "lines": [ "line B P A'", "line B D", "line A C A'", "line C P D" ], "circles": [], "semantics": [ "BD \\perp CD on D", "AA' \\perp CD on C" ] }, { "diagram": "PGDP/printed/image/MathVR_40681_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "O", "D" ], "lines": [ "line A O", "line A D B", "line O D C", "line C B" ], "circles": [ "\\odot O lieson B C A" ], "semantics": [ "AB \\perp OC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_75310_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "F", "E", "D" ], "lines": [ "line C E B", "line D C", "line A E", "line A B F", "line D E F", "line D A" ], "circles": [], "semantics": [ "CB \\perp DC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_33296_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "O", "D" ], "lines": [ "line D C", "line B O D", "line A E D", "line B C", "line A O C", "line E O", "line A B" ], "circles": [], "semantics": [ "AC \\perp EO on O" ] }, { "diagram": "PGDP/printed/image/MathVR_55959_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "H", "C", "E", "D", "F" ], "lines": [ "line E C", "line F H C", "line D C", "line A F D", "line B C", "line E H", "line F E", "line A E B" ], "circles": [], "semantics": [ "EC \\perp EH on E", "FC \\perp EH on H" ] }, { "diagram": "PGDP/printed/image/MathVR_1936_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "O", "D" ], "lines": [ "line O A", "line O D C", "line A D B" ], "circles": [ "\\odot O lieson B C A" ], "semantics": [ "OC \\perp AB on D" ] }, { "diagram": "PGDP/printed/image/MathVR_33937_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "A", "E" ], "lines": [ "line A B", "line A C", "line D A", "line A E", "line B E", "line D C", "line B C" ], "circles": [], "semantics": [ "m \\angle BAD = m \\angle 1", "m \\angle CAE = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_77720_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "E", "C", "O", "N", "M" ], "lines": [ "line A M C", "line B N A", "line B O M", "line B D E C", "line A O D", "line O E", "line N O C" ], "circles": [], "semantics": [ "BC \\perp OE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_46744_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "O", "E", "D" ], "lines": [ "line D E C", "line A O B", "line A D", "line B C", "line O E" ], "circles": [ "\\odot O lieson A E B" ], "semantics": [ "DC \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_63857_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "C" ], "lines": [ "line D A", "line C B", "line A B", "line D C" ], "circles": [], "semantics": [ "DA \\perp DC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_62822_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "E" ], "lines": [ "line D B", "line C E D", "line A E", "line A C", "line E B" ], "circles": [], "semantics": [ "CD \\perp AC on C", "DB \\perp CD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_82985_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "P", "E", "A", "D" ], "lines": [ "line A P", "line D B", "line A B", "line C B P E", "line A D", "line D E", "line A C", "line D P" ], "circles": [], "semantics": [ "DE = b", "BE = b", "AC = a", "CB = a" ] }, { "diagram": "PGDP/printed/image/MathVR_15130_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "D", "B", "F", "C", "H" ], "lines": [ "line C B", "line A F C", "line D C", "line A E B", "line D A", "line F H B", "line C H E" ], "circles": [], "semantics": [ "FB \\perp CE on H" ] }, { "diagram": "PGDP/printed/image/MathVR_2456_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "O", "C", "E", "A" ], "lines": [ "line O E", "line A E C", "line A O B", "line A D", "line B E", "line B D C", "line E D", "line O D" ], "circles": [ "\\odot O lieson A E D B" ], "semantics": [ "m \\angle HBF = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_40437_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "Q", "P", "O", "M", "N", "B" ], "lines": [ "line B P Q", "line O B", "line M Q", "line M A", "line A O", "line M O P N", "line O Q", "line A P" ], "circles": [ "\\odot O lieson M A B N Q" ], "semantics": [ "m \\angle AMO = 30", "m \\angle BOP = 30", "m \\angle QMO = 30", "m \\angle POQ = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_81865_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "E", "O", "B", "F" ], "lines": [ "line A F", "line A C", "line A O E B", "line F C", "line C B", "line C E D", "line B D" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [ "CF \\perp AF on F", "CD \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_54533_img4.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "A", "D", "T", "E" ], "lines": [ "line E A", "line T D E", "line D M", "line T M", "line M A" ], "circles": [], "semantics": [ "TE \\perp TM on T" ] }, { "diagram": "PGDP/printed/image/MathVR_75262_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "N", "M", "C" ], "lines": [ "line C D B", "line M B", "line C N", "line A N D M", "line A B", "line C A" ], "circles": [], "semantics": [ "MB \\perp AM on M", "CN \\perp AM on N" ] }, { "diagram": "PGDP/printed/image/MathVR_12217_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "R", "Q", "O", "A", "D", "P", "B" ], "lines": [ "line C R A", "line C D", "line C Q B", "line A D P B" ], "circles": [ "\\odot O lieson R Q P" ], "semantics": [ "AB \\perp CD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_56686_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "B", "D", "C", "F" ], "lines": [ "line D C", "line A B", "line F B", "line D E", "line F D A", "line C B E" ], "circles": [], "semantics": [ "m \\angle CDE = m \\angle 2", "m \\angle FBC = m \\angle 3", "m \\angle FBA = m \\angle 4", "m \\angle EDA = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_9665_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "E", "C", "A" ], "lines": [ "line A C", "line A E D", "line B D", "line A B", "line B E C", "line D C" ], "circles": [], "semantics": [ "BD \\perp DC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_62774_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "C", "D", "O" ], "lines": [ "line B D C", "line A C", "line B A", "line B E", "line A D", "line A O E" ], "circles": [ "\\odot O lieson A C E B" ], "semantics": [ "BC \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_32291_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "E", "A", "D", "P", "F", "C", "B" ], "lines": [ "line F P", "line O D F B", "line O P C", "line O E A", "line P E", "line D P" ], "circles": [], "semantics": [ "FP \\perp OB on F", "OA \\perp PE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_70348_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "O", "C", "D", "E", "A" ], "lines": [ "line A O E C", "line F D E", "line B F", "line O D", "line A B", "line B D C" ], "circles": [ "\\odot O lieson A E D" ], "semantics": [ "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_81005_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "M", "N" ], "lines": [ "line A M B", "line A E D", "line B N C", "line C D", "line E M", "line M N", "line E N" ], "circles": [], "semantics": [ "m \\angle AEM = m \\angle \\alpha" ] }, { "diagram": "PGDP/printed/image/MathVR_44101_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B" ], "lines": [ "line B C", "line D B", "line A B", "line D A C" ], "circles": [], "semantics": [ "BA = 2", "BC = 1", "m \\angle BDA = 15", "m \\angle BAC = 30" ] }, { "diagram": "PGDP/printed/image/MathVR_44609_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "E", "F", "O", "A", "B", "M" ], "lines": [ "line E B", "line M E F N", "line A O B", "line A F" ], "circles": [ "\\odot O lieson A M B N" ], "semantics": [ "AF \\perp MN on F", "EB \\perp MN on E" ] }, { "diagram": "PGDP/printed/image/MathVR_66508_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "E", "B", "A", "C", "F", "O", "D" ], "lines": [ "line H E", "line D O C", "line A D", "line B E C", "line O E", "line A F H B" ], "circles": [ "\\odot O lieson F D C E" ], "semantics": [ "HE \\perp AB on H" ] }, { "diagram": "PGDP/printed/image/MathVR_32263_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "D", "F" ], "lines": [ "line E C", "line F C", "line D C", "line A F D", "line B C", "line F E", "line A E B" ], "circles": [], "semantics": [ "EC \\perp FE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_74495_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "F", "P", "G" ], "lines": [ "line A F C", "line B P", "line P E", "line G P", "line B E C", "line F P", "line A G B", "line P C", "line A P" ], "circles": [], "semantics": [ "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_14728_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "C", "B", "A", "F", "G", "D" ], "lines": [ "line a lieson A E", "line b lieson C F", "line A G B", "line C G D", "line c lieson A C" ], "circles": [], "semantics": [ "m \\angle GCA = m \\angle 2", "m \\angle GAC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_18058_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "O", "A", "E" ], "lines": [ "line C O", "line C E D", "line A O E B" ], "circles": [ "\\odot O lieson A D B C" ], "semantics": [ "CD \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_73439_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "O" ], "lines": [ "line A F D", "line D C", "line A O C", "line B F", "line B O D", "line B E C", "line A B", "line D E", "line F O E" ], "circles": [], "semantics": [ "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_75864_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "O", "B", "D", "C" ], "lines": [ "line D E", "line C B", "line A D C", "line A E O B", "line D O", "line C O" ], "circles": [], "semantics": [ "m \\angle BOC = m \\angle 6", "m \\angle EDO = m \\angle 3", "m \\angle BCO = m \\angle 2", "m \\angle DCO = m \\angle 1", "m \\angle DEO = m \\angle 5", "m \\angle DOC = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/MathVR_56681_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "G", "P", "C", "F", "E", "D", "A" ], "lines": [ "line A E", "line D E C", "line A D", "line F E", "line G B P C", "line A F P", "line A G", "line A B" ], "circles": [], "semantics": [ "FE \\perp AP on F" ] }, { "diagram": "PGDP/printed/image/MathVR_81507_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "M", "C", "F", "D" ], "lines": [ "line E F", "line D E", "line B E C M", "line A F C", "line A D B" ], "circles": [], "semantics": [ "BM \\perp AB on B", "EF \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_4418_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B" ], "lines": [ "line C D B", "line A B", "line C A", "line A D" ], "circles": [], "semantics": [ "CB \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_39667_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "D", "F", "C", "B" ], "lines": [ "line A B", "line B F", "line C F D", "line B E", "line C B", "line A E D" ], "circles": [], "semantics": [ "CD \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_70852_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "D" ], "lines": [ "line A D", "line D C", "line D E", "line B C", "line A E C", "line A B" ], "circles": [], "semantics": [ "AC \\perp AB on A", "DE \\perp AC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_23209_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "F", "D", "A" ], "lines": [ "line A D C", "line B D", "line B F C", "line D F", "line A E B", "line E D" ], "circles": [], "semantics": [ "BC \\perp DF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_82021_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "G", "F", "C", "H", "D" ], "lines": [ "line D C", "line B F E", "line F H G", "line A E D", "line F D", "line B H D", "line B G C", "line A B" ], "circles": [], "semantics": [ "FG \\perp FD on F" ] }, { "diagram": "PGDP/printed/image/MathVR_14226_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "B", "D", "C", "A", "E" ], "lines": [ "line A D E", "line A C", "line E C", "line A F", "line B F C", "line D C", "line B A" ], "circles": [], "semantics": [ "AC \\perp BA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_7059_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "O" ], "lines": [ "line A D", "line A O C", "line A E B", "line D C", "line D O B", "line C B", "line C E" ], "circles": [], "semantics": [ "CB \\perp AC on C", "AB \\perp CE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_37318_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "O", "D" ], "lines": [ "line B C O", "line C D", "line A D O", "line B A" ], "circles": [], "semantics": [ "CD \\perp AO on D", "BO \\perp BA on B" ] }, { "diagram": "PGDP/printed/image/MathVR_1655_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "B", "A", "C", "F", "E", "D", "H" ], "lines": [ "line D E C", "line B F D", "line F H G", "line A D", "line B H E", "line B G C", "line A B", "line F E" ], "circles": [], "semantics": [ "FG \\perp BE on H" ] }, { "diagram": "PGDP/printed/image/MathVR_70064_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C", "M", "N" ], "lines": [ "line A N C", "line M D", "line B D C", "line N D", "line A M B", "line A D", "line M N" ], "circles": [], "semantics": [ "m \\angle NAD = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_17239_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "D", "B", "E", "C", "A" ], "lines": [ "line A C", "line E D F A", "line B E", "line F C", "line B A", "line B D C" ], "circles": [], "semantics": [ "EA \\perp BE on E", "EA \\perp FC on F" ] }, { "diagram": "PGDP/printed/image/MathVR_31378_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "F", "H", "E", "D", "G" ], "lines": [ "line A D", "line D C", "line B F E", "line A F G", "line G H D", "line B C", "line A B", "line E H C" ], "circles": [], "semantics": [ "m \\angle FAB = m \\angle 1", "m \\angle FBA = m \\angle 3", "m \\angle FBC = m \\angle 4", "m \\angle DAF = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_81692_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "C", "D", "F", "A" ], "lines": [ "line A D", "line F D C", "line A F", "line B E C", "line A B", "line A E" ], "circles": [], "semantics": [ "BC \\perp AE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_82273_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "C", "D", "A" ], "lines": [ "line A C", "line B D A", "line D E", "line B E C", "line D C" ], "circles": [], "semantics": [ "AC \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_36485_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "D", "C", "A", "B", "F" ], "lines": [ "line D B", "line F D", "line D E", "line A D", "line C E B", "line A B", "line A F C" ], "circles": [], "semantics": [ "FD \\perp AC on F", "DE \\perp CB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_79050_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "E", "F", "P" ], "lines": [ "line C F B", "line A E C", "line E F", "line E P", "line A P B", "line C P", "line P F" ], "circles": [], "semantics": [ "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_37142_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "F", "B", "A", "C", "E", "G", "H" ], "lines": [ "line F E", "line D H E", "line A D", "line B G H", "line B C E", "line D G C", "line A B", "line G F", "line G E" ], "circles": [], "semantics": [ "m \\angle HDG = m \\angle 2", "m \\angle GBC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_76240_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "P", "O" ], "lines": [ "line A O D", "line A C", "line B A P", "line B O", "line B D C", "line C O", "line C P", "line D O", "line P O" ], "circles": [], "semantics": [ "AD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_5045_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "D" ], "lines": [ "line D C", "line B E D", "line A D", "line A E", "line B C", "line A B" ], "circles": [], "semantics": [ "m \\angle EDA = m \\angle \\theta" ] }, { "diagram": "PGDP/printed/image/MathVR_55425_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "O", "B", "A", "P" ], "lines": [ "line C P", "line A C", "line A O B P" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "m \\angle CAO = 30" ] }, { "diagram": "PGDP/printed/image/MathVR_20928_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H" ], "lines": [ "line A H B", "line A E", "line A D", "line B E C", "line C G D", "line C F", "line E H", "line E G F" ], "circles": [], "semantics": [ "EF \\perp AE on E", "m \\angle EAH = m \\angle 1", "m \\angle GEC = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_77500_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "H", "G", "F", "D", "N", "M", "A", "B" ], "lines": [ "line A M B", "line C H D", "line E M H F", "line M N", "line G H" ], "circles": [], "semantics": [ "m \\angle HMN = m \\angle 1", "m \\angle MHG = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_15267_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D" ], "lines": [ "line C B", "line A D B", "line A C", "line C D" ], "circles": [], "semantics": [ "m \\angle BCA = 105", "m \\angle DAC = 30" ] }, { "diagram": "PGDP/printed/image/MathVR_2614_image1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "C", "B", "D", "F" ], "lines": [ "line D E", "line F E", "line A E B", "line C D B", "line C F A", "line F D" ], "circles": [], "semantics": [ "DE \\perp FD on D", "AB \\perp CA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_10237_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "B", "A", "C", "E", "D", "M" ], "lines": [ "line D C", "line A D", "line A M", "line B F C", "line A E B", "line E M C", "line D M F" ], "circles": [], "semantics": [ "EC \\perp DF on M" ] }, { "diagram": "PGDP/printed/image/MathVR_62513_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "O", "B", "C", "A" ], "lines": [ "line B E C", "line A C", "line A E O D", "line B O", "line B D", "line B A" ], "circles": [ "\\odot O lieson B A C D" ], "semantics": [ "BC \\perp AD on E" ] }, { "diagram": "PGDP/printed/image/MathVR_32852_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "B", "C", "P", "D", "A" ], "lines": [ "line A C", "line B P A", "line B Q D C", "line A D", "line A Q", "line P Q" ], "circles": [], "semantics": [ "BC \\perp PQ on Q" ] }, { "diagram": "PGDP/printed/image/MathVR_73983_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line D C", "line B D", "line A D", "line B C", "line A B" ], "circles": [], "semantics": [ "AD \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_16572_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "O", "P", "D", "C", "B" ], "lines": [ "line B D", "line O B", "line A D", "line A P", "line B C A", "line O C D P", "line O A" ], "circles": [ "\\odot O lieson B D A" ], "semantics": [ "BA \\perp OP on C" ] }, { "diagram": "PGDP/printed/image/MathVR_14239_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "E", "A", "C", "M", "N" ], "lines": [ "line A E N", "line E C", "line M A B", "line A D", "line B D C", "line A C" ], "circles": [], "semantics": [ "AN \\perp EC on E", "AD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_3279_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "O" ], "lines": [ "line A E B", "line A D", "line B C", "line B D", "line C F D" ], "circles": [], "semantics": [ "DB \\perp DA on D" ] }, { "diagram": "PGDP/printed/image/MathVR_67722_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "A", "G", "D", "B", "H", "C" ], "lines": [ "line D G C", "line H A", "line C B", "line D H", "line D E", "line A E B", "line F G", "line F H E", "line D F", "line D A" ], "circles": [], "semantics": [ "DC \\perp FG on G" ] }, { "diagram": "PGDP/printed/image/MathVR_8565_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B", "E", "O" ], "lines": [ "line A O B", "line C E A", "line C D B", "line E D" ], "circles": [ "\\odot O lieson A D B" ], "semantics": [ "CA \\perp ED on E" ] }, { "diagram": "PGDP/printed/image/MathVR_23100_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "E" ], "lines": [ "line A D", "line E D", "line A C", "line A E", "line B C D", "line A B" ], "circles": [], "semantics": [ "AC \\perp BD on C" ] }, { "diagram": "PGDP/printed/image/MathVR_38479_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "B", "P", "A", "C", "N", "D" ], "lines": [ "line D C", "line B N P D", "line N Q", "line A D", "line B Q C", "line P Q", "line A B" ], "circles": [], "semantics": [ "BD \\perp NQ on N" ] }, { "diagram": "PGDP/printed/image/MathVR_27749_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "O" ], "lines": [ "line A D", "line A B", "line A O C", "line B D", "line B E", "line B C", "line E C D" ], "circles": [ "\\odot O lieson A D C B" ], "semantics": [ "ED \\perp BE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_79448_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "F", "A", "E", "D" ], "lines": [ "line A E", "line B A D", "line A C", "line B C F", "line E C" ], "circles": [], "semantics": [ "m \\angle ACB = m \\angle 2", "m \\angle BAC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_13604_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "B", "C", "E", "G", "D", "A" ], "lines": [ "line A D C", "line B G D", "line B F C", "line E F", "line A E B", "line E D", "line E G C" ], "circles": [], "semantics": [ "BD \\perp EC on G" ] }, { "diagram": "PGDP/printed/image/MathVR_41874_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line C B", "line A C", "line A B" ], "circles": [], "semantics": [ "CB \\perp AB on B", "CA = l", "BC = h", "m \\angle CAB = m \\angle \\theta" ] }, { "diagram": "PGDP/printed/image/MathVR_80961_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "C", "H", "F", "O", "D", "P" ], "lines": [ "line D C", "line B O F D", "line P O", "line A P D", "line P F", "line D H", "line B C", "line A E O H C", "line P E", "line A B" ], "circles": [], "semantics": [ "DH \\perp AC on H" ] }, { "diagram": "PGDP/printed/image/MathVR_2149_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D", "O" ], "lines": [ "line O C", "line C B", "line A O B", "line A D C", "line D O" ], "circles": [ "\\odot O lieson A B C" ], "semantics": [ "AC \\perp DO on D" ] }, { "diagram": "PGDP/printed/image/MathVR_4182_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "O", "A" ], "lines": [ "line B O", "line A C", "line O D", "line B D C", "line A B" ], "circles": [], "semantics": [ "OD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_76195_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "P", "O", "B", "E", "D", "C", "F" ], "lines": [ "line O D A", "line D F P", "line D E", "line O F E C", "line O P B" ], "circles": [], "semantics": [ "OA \\perp DE on D" ] }, { "diagram": "PGDP/printed/image/MathVR_30708_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "D", "B", "Q", "E", "C", "O", "A" ], "lines": [ "line A Q C", "line A O D", "line Q O P", "line B P D E C", "line Q E", "line Q D", "line A B" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "AD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_13836_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "M", "C", "N", "O", "D", "P" ], "lines": [ "line D C", "line B O N D", "line A P D", "line P N", "line P O", "line B C", "line A M O C", "line A B", "line P M" ], "circles": [], "semantics": [ "AC \\perp PM on M", "BD \\perp PN on N" ] }, { "diagram": "PGDP/printed/image/MathVR_82100_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "F", "E", "P", "C" ], "lines": [ "line B C", "line A E", "line C D", "line F C", "line A D", "line B E F D", "line B P A" ], "circles": [], "semantics": [ "CD \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_76140_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "E", "A", "C" ], "lines": [ "line A C", "line B D E C", "line A E", "line A D", "line A B" ], "circles": [], "semantics": [ "AB = c = x", "AE = \\frac{\\sqrt{3} }{2} x" ] }, { "diagram": "PGDP/printed/image/MathVR_72993_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B", "C'" ], "lines": [ "line C' D", "line A D", "line C D B", "line A C' B", "line A C" ], "circles": [], "semantics": [ "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_62202_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "E", "A" ], "lines": [ "line A E C", "line A D", "line B D C", "line A B", "line D E" ], "circles": [], "semantics": [ "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_55520_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "B", "F", "A", "C" ], "lines": [ "line D C", "line A D", "line B E F C", "line D F", "line D E", "line A B" ], "circles": [], "semantics": [ "BC \\perp DF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_27574_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "N", "B", "A", "C", "O", "E", "D", "P" ], "lines": [ "line A M D", "line B N C", "line D C", "line N P O D", "line A N", "line M O C", "line M E N", "line A B", "line E P C" ], "circles": [], "semantics": [ "m \\angle CNP = m \\angle 4", "m \\angle MDO = m \\angle 1", "m \\angle NCP = m \\angle 2", "m \\angle PNE = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_5435_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "C", "O", "B", "D" ], "lines": [ "line E D", "line E C A", "line A O B" ], "circles": [ "\\odot O lieson A C D B" ], "semantics": [ "ED \\perp EA on E" ] }, { "diagram": "PGDP/printed/image/MathVR_11955_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "D", "C", "A", "H" ], "lines": [ "line A C", "line B E H C", "line B D A", "line A H", "line D C", "line D E" ], "circles": [], "semantics": [ "BC \\perp AH on H", "BC \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_31231_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "M", "F", "B", "C", "D" ], "lines": [ "line D C", "line A D", "line A M E", "line A B", "line B M F C", "line D F E" ], "circles": [], "semantics": [ "AE \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_15530_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "E" ], "lines": [ "line B E A", "line C A", "line B D C", "line D E" ], "circles": [], "semantics": [ "BC \\perp DE on D" ] }, { "diagram": "PGDP/printed/image/MathVR_79723_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "O", "P" ], "lines": [ "line C P B", "line O D B", "line O P", "line A P D", "line A B", "line O C A" ], "circles": [], "semantics": [ "OP \\perp AD on P" ] }, { "diagram": "PGDP/printed/image/MathVR_20718_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "F", "B", "D", "H", "C" ], "lines": [ "line C F B", "line C D H A", "line D E", "line H E", "line A E B", "line D F" ], "circles": [], "semantics": [ "DE \\perp DF on D" ] }, { "diagram": "PGDP/printed/image/MathVR_7866_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "C", "B", "D" ], "lines": [ "line C B", "line A D C", "line D E", "line A E B", "line D B" ], "circles": [], "semantics": [ "DE \\perp AB on E", "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_39824_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "D", "H", "B", "E", "C" ], "lines": [ "line E F B", "line C B", "line E H A", "line D E C", "line D H F", "line A B", "line D A", "line A F C" ], "circles": [], "semantics": [ "m \\angle FBC = m \\angle 4", "m \\angle HAD = m \\angle 3", "m \\angle FBA = m \\angle 2", "m \\angle HDA = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_76798_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "A", "H", "D", "B", "E", "G", "C" ], "lines": [ "line D H G", "line C G B", "line A E H C", "line D C", "line D E F", "line A F B", "line E G", "line D A", "line G F" ], "circles": [], "semantics": [ "DF \\perp EG on E" ] }, { "diagram": "PGDP/printed/image/MathVR_70794_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "C", "D", "B", "A", "E", "G" ], "lines": [ "line E B", "line G B", "line D A M G", "line C B", "line M B", "line A B", "line A E", "line D E C" ], "circles": [], "semantics": [ "DG \\perp MB on M", "m \\angle EBA = 45" ] }, { "diagram": "PGDP/printed/image/MathVR_1204_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "M", "G", "N", "C" ], "lines": [ "line C N B", "line A B", "line C M A", "line M G N" ], "circles": [], "semantics": [ "CB \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_70175_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "C", "D", "O", "E", "M" ], "lines": [ "line C M D", "line E O M F", "line E C", "line F D" ], "circles": [ "\\odot O lieson E D F C" ], "semantics": [ "CD \\perp EF on M" ] }, { "diagram": "PGDP/printed/image/MathVR_55689_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "G", "O" ], "lines": [ "line O A", "line O G", "line A G B", "line O B" ], "circles": [], "semantics": [ "OG \\perp AB on G" ] }, { "diagram": "PGDP/printed/image/MathVR_52407_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "B", "E", "C" ], "lines": [ "line B A", "line E C B", "line C D", "line E D A" ], "circles": [], "semantics": [ "BA \\perp EB on B", "CD \\perp EA on D", "m \\angle BCD = 120" ] }, { "diagram": "PGDP/printed/image/MathVR_66884_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "B", "C", "N", "A" ], "lines": [ "line A N C", "line B M C", "line A B", "line M N" ], "circles": [], "semantics": [ "AC \\perp MN on N" ] }, { "diagram": "PGDP/printed/image/MathVR_8278_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A" ], "lines": [ "line B A", "line B C" ], "circles": [], "semantics": [ "m \\angle ABC = 30" ] }, { "diagram": "PGDP/printed/image/MathVR_22311_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "E", "B", "D" ], "lines": [ "line A B", "line C E B", "line E D", "line C D A", "line D B" ], "circles": [], "semantics": [ "AB \\perp CA on A", "CB \\perp ED on E" ] }, { "diagram": "PGDP/printed/image/MathVR_10799_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "A", "B", "E", "G", "F" ], "lines": [ "line A D B E", "line F E", "line A C", "line D G F", "line C G B" ], "circles": [], "semantics": [ "AE \\perp CB on B", "AE \\perp FE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_4217_image2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "H", "F", "O", "P", "D" ], "lines": [ "line D C", "line B O F D", "line P O", "line P F", "line A P D", "line D H", "line B C", "line A E O H C", "line A B", "line P E" ], "circles": [], "semantics": [ "AC \\perp PE on E", "BD \\perp PF on F", "DH \\perp AC on H" ] }, { "diagram": "PGDP/printed/image/MathVR_22356_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "M", "P", "F", "O", "A", "B", "C" ], "lines": [ "line C B", "line D B", "line C P O", "line A P D", "line C F M", "line A F O B" ], "circles": [ "\\odot O lieson A C D B M" ], "semantics": [ "CM \\perp AB on F" ] }, { "diagram": "PGDP/printed/image/MathVR_66880_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "C", "B", "N", "A" ], "lines": [ "line C M A", "line B N A", "line B C", "line N M" ], "circles": [], "semantics": [ "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_46769_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "O", "A", "D", "E", "B", "C" ], "lines": [ "line C B", "line C O D E F", "line O B", "line A O", "line C A", "line A D B", "line B F" ], "circles": [ "\\odot O lieson C B E A" ], "semantics": [ "CF \\perp AB on D" ] }, { "diagram": "PGDP/printed/image/MathVR_27987_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "C", "O", "A", "P" ], "lines": [ "line A C", "line B O P", "line A O E", "line A P", "line B E C", "line A B" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "AE \\perp BC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_7858_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "E", "F", "D", "O", "B", "G" ], "lines": [ "line A D", "line E B O A", "line E C F D", "line A G F", "line A C" ], "circles": [ "\\odot O lieson A G C B" ], "semantics": [ "ED \\perp AF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_47807_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "G", "B", "C", "E", "O", "F", "D" ], "lines": [ "line A F C", "line B E A", "line E O", "line B G D C", "line A O D", "line E G" ], "circles": [ "\\odot O lieson E A F D" ], "semantics": [ "BC \\perp EG on G" ] }, { "diagram": "PGDP/printed/image/MathVR_52773_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "O" ], "lines": [ "line A B", "line A E", "line A O C", "line A D", "line B E C", "line C D", "line B O D" ], "circles": [], "semantics": [ "AE \\perp BC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_17529_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "P", "Q", "M" ], "lines": [ "line D C", "line P Q", "line A P D", "line B M Q C", "line D M", "line A B" ], "circles": [], "semantics": [ "BC \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_15956_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "Q", "B", "E", "P", "O" ], "lines": [ "line A O B", "line A E Q", "line D A", "line C Q B", "line D P E B", "line A P", "line D C" ], "circles": [ "\\odot O lieson P A B Q" ], "semantics": [ "m \\angle QBE = m \\angle 2", "m \\angle ADP = m \\angle 3", "m \\angle EAP = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_45416_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "O", "A", "B", "C" ], "lines": [ "line C D B", "line D O", "line C A", "line A O B" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "CB \\perp DO on D" ] }, { "diagram": "PGDP/printed/image/MathVR_56100_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "M", "C" ], "lines": [ "line C B", "line A M", "line A B", "line C M", "line C A", "line M B" ], "circles": [], "semantics": [ "m \\angle ABM = 30", "m \\angle MAB = 10" ] }, { "diagram": "PGDP/printed/image/MathVR_5811_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "B", "A", "C", "Q", "D" ], "lines": [ "line A Q", "line D Q C", "line A D", "line P Q", "line A P", "line B P C", "line A B" ], "circles": [], "semantics": [ "PQ \\perp AP on P", "CQ = b", "BP = b", "AD = a+b", "DQ = a-b", "AB = a", "PC = a", "m \\angle PAB = m \\angle \\alpha", "m \\angle DAQ = m \\angle \\beta" ] }, { "diagram": "PGDP/printed/image/MathVR_5053_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D" ], "lines": [ "line C D", "line C B", "line A D B", "line A C" ], "circles": [], "semantics": [ "CD \\perp AB on D" ] }, { "diagram": "PGDP/printed/image/MathVR_64508_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "B" ], "lines": [ "line A D B", "line C B", "line C A", "line C D" ], "circles": [], "semantics": [ "CB \\perp CA on C", "AB \\perp CD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_32366_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C", "M", "P", "O" ], "lines": [ "line O C", "line P C", "line B A P", "line A O D", "line O M P", "line B D C", "line A M C" ], "circles": [], "semantics": [ "AD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_62890_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "C", "D", "O", "B" ], "lines": [ "line E C B", "line C O", "line E D A", "line D C", "line A O B" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "CO \\perp DC on C", "EA \\perp DC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_58467_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C", "H", "E" ], "lines": [ "line A E C", "line B A", "line B H E", "line B D C", "line A H D" ], "circles": [], "semantics": [ "AC \\perp BE on E", "BC \\perp AD on D", "m \\angle HBD = m \\angle 2", "m \\angle EAH = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_20586_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "B'", "C", "C'", "A" ], "lines": [ "line C' B", "line A C", "line B' A", "line B' C'", "line C' A", "line B C", "line B A" ], "circles": [], "semantics": [ "B'C' \\perp C'A on C'", "AC \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_3699_image1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "B", "F", "C", "D" ], "lines": [ "line C B", "line D C", "line A E B", "line F B", "line D E", "line D F A" ], "circles": [], "semantics": [ "FB \\perp DA on F", "AB \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_6870_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "O", "D" ], "lines": [ "line A D", "line D C", "line B E O D", "line A E", "line B C", "line A O C", "line A B" ], "circles": [], "semantics": [ "BD \\perp AE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_73907_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "F", "G", "C", "D", "O", "A", "B", "P" ], "lines": [ "line G O", "line F O", "line A E G F P", "line A D O B C" ], "circles": [ "\\odot O lieson D E F B" ], "semantics": [ "GO \\perp AP on G" ] }, { "diagram": "PGDP/printed/image/MathVR_4559_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "Q", "C", "P", "F", "A" ], "lines": [ "line A F C", "line Q F", "line E F", "line B E C", "line P E", "line A Q P B" ], "circles": [], "semantics": [ "BC \\perp PE on E", "AC \\perp EF on F", "QF \\perp AB on Q" ] }, { "diagram": "PGDP/printed/image/MathVR_74799_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "F", "D", "E" ], "lines": [ "line A D", "line E D", "line D C", "line B D", "line B F C", "line D F", "line E A B" ], "circles": [], "semantics": [ "BC \\perp DF on F", "ED \\perp EB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_37979_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "I", "D", "E", "N", "F", "M", "C", "B", "G", "A" ], "lines": [ "line D E", "line H G", "line G F", "line I N H", "line I C", "line D C", "line A N C", "line I M D", "line A B", "line B M C", "line E F" ], "circles": [], "semantics": [ "m \\angle DCM = m \\angle 1", "m \\angle ICN = m \\angle 3", "m \\angle ICM = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_54384_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "O", "D", "B" ], "lines": [ "line B D C", "line B O A", "line A D", "line A C", "line O D" ], "circles": [ "\\odot O lieson D A" ], "semantics": [ "BC \\perp AC on C", "m \\angle OAD = m \\angle 1", "m \\angle ADO = m \\angle 2", "m \\angle DAC = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_12891_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "A'", "B", "D", "C", "E" ], "lines": [ "line C B", "line D E", "line A D C", "line A E B", "line A' E", "line A' D" ], "circles": [], "semantics": [ "m \\angle CDA' = m \\angle 1", "m \\angle BEA' = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_77638_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "F", "A", "E", "D", "G", "B" ], "lines": [ "line A E B", "line E G", "line E F", "line F G", "line C F D" ], "circles": [], "semantics": [ "m \\angle EFG = m \\angle 2", "m \\angle GEF = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_45284_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "Q", "A", "O", "P" ], "lines": [ "line P C", "line P Q", "line C Q A", "line B P A", "line O P", "line B O C" ], "circles": [ "\\odot O lieson B P C" ], "semantics": [ "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_51950_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "B", "A", "C", "F" ], "lines": [ "line D C", "line A D", "line E F", "line A E", "line B E C", "line A B", "line C F" ], "circles": [], "semantics": [ "EF \\perp AE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_41045_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A" ], "lines": [ "line B C", "line B A", "line A C" ], "circles": [], "semantics": [ "m \\angle BAC = 120" ] }, { "diagram": "PGDP/printed/image/MathVR_4954_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "M", "B", "N", "A", "G", "C", "D" ], "lines": [ "line A N D", "line E N C", "line D C", "line N M", "line A M", "line B M G C", "line N G", "line A E", "line A B" ], "circles": [], "semantics": [ "BC \\perp NG on G" ] }, { "diagram": "PGDP/printed/image/MathVR_67654_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "Q", "B", "A", "P" ], "lines": [ "line Q P", "line B C", "line Q C", "line C A", "line B P A", "line B Q" ], "circles": [], "semantics": [ "BC \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_37304_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "C", "D", "A", "F", "B" ], "lines": [ "line B F D", "line A E", "line C E D", "line A B", "line A C", "line A F", "line B E" ], "circles": [], "semantics": [ "BD \\perp AF on F", "CD \\perp AC on C", "BD \\perp CD on D", "m \\angle DEB = 66", "m \\angle AEC = 55" ] }, { "diagram": "PGDP/printed/image/MathVR_9429_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "O", "D" ], "lines": [ "line A D", "line D C", "line B E O D", "line A E", "line B C", "line A O C", "line A B" ], "circles": [], "semantics": [ "BD \\perp AE on E", "m \\angle EAO = m \\angle 2", "m \\angle EAB = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_47506_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "M", "D", "F", "C", "H", "E", "O" ], "lines": [ "line B O D C", "line A E C", "line B F A", "line B H E", "line A M H D" ], "circles": [ "\\odot O lieson B F M E C" ], "semantics": [ "BC \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_56049_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "C", "B", "D" ], "lines": [ "line C B", "line A E D B", "line C D", "line A C", "line C E" ], "circles": [], "semantics": [ "AB \\perp CE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_49966_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "D", "C", "A", "B", "F" ], "lines": [ "line F B C", "line A F", "line A E", "line D E C", "line A D", "line A B" ], "circles": [], "semantics": [ "AF \\perp AE on A" ] }, { "diagram": "PGDP/printed/image/MathVR_22676_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "O", "A", "B", "C" ], "lines": [ "line O C D", "line A O", "line A C B" ], "circles": [ "\\odot O lieson B D A" ], "semantics": [ "OD \\perp AB on C" ] }, { "diagram": "PGDP/printed/image/MathVR_54768_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "F", "C" ], "lines": [ "line A C", "line A F B", "line B E C", "line A E", "line F C" ], "circles": [], "semantics": [ "AB \\perp FC on F", "BC \\perp AE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_78316_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "F", "A", "D" ], "lines": [ "line A F C", "line A D", "line B D F", "line A E B", "line E D C" ], "circles": [], "semantics": [ "m \\angle DAE = m \\angle 1", "m \\angle FAD = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_32160_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "E", "C" ], "lines": [ "line D C", "line A E D", "line A B", "line B C", "line D B", "line E B" ], "circles": [], "semantics": [ "AD \\perp EB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_14789_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line A C", "line B D C", "line B A", "line A D" ], "circles": [], "semantics": [ "BC \\perp AD on D", "AB = 6" ] }, { "diagram": "PGDP/printed/image/MathVR_11787_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "A", "B", "D" ], "lines": [ "line C D", "line B C", "line A E D", "line B E", "line B A" ], "circles": [], "semantics": [ "BE = h", "BA = x" ] }, { "diagram": "PGDP/printed/image/MathVR_16946_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "B" ], "lines": [ "line A D B", "line A C", "line D C", "line B C" ], "circles": [], "semantics": [ "m \\angle ACD = 45", "m \\angle DCB = 32" ] }, { "diagram": "PGDP/printed/image/MathVR_4441_image2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "A", "D" ], "lines": [ "line A C", "line B E A", "line E D", "line B D C", "line A D" ], "circles": [], "semantics": [ "BA \\perp ED on E", "AC \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_23567_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "M", "D", "C", "N", "E" ], "lines": [ "line D N E", "line A E C", "line A D B", "line B M C", "line A N M" ], "circles": [], "semantics": [ "DE \\perp AM on N", "BC \\perp AM on M" ] }, { "diagram": "PGDP/printed/image/MathVR_3772_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "Q", "D", "P" ], "lines": [ "line C D B", "line C P", "line A P D", "line A B", "line Q P", "line C Q A" ], "circles": [], "semantics": [ "CB \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_30568_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "G", "E", "D", "A", "B", "C" ], "lines": [ "line C F B", "line A E F", "line C E D G", "line C A", "line A D B", "line B G" ], "circles": [], "semantics": [ "CB \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_3388_image2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "O", "E", "D", "B", "C" ], "lines": [ "line C D B", "line A D", "line D E", "line D O", "line C A", "line A O E B" ], "circles": [ "\\odot O lieson A D E" ], "semantics": [ "AD \\perp DE on D", "CB \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_61814_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "B", "O", "D", "A" ], "lines": [ "line A B E C D", "line E O" ], "circles": [ "\\odot O lieson B C", "\\odot O lieson A D" ], "semantics": [ "AD \\perp EO on E" ] }, { "diagram": "PGDP/printed/image/MathVR_80832_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "E", "B", "A", "C", "N", "O", "D" ], "lines": [ "line M E", "line O N C", "line D C", "line E N", "line O M B", "line A O D", "line B E C", "line A B" ], "circles": [], "semantics": [ "ME \\perp OB on M", "OC \\perp EN on N" ] }, { "diagram": "PGDP/printed/image/MathVR_77116_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line B E A", "line B F D", "line C E", "line C D A", "line B C", "line F A" ], "circles": [], "semantics": [ "BD \\perp CA on D" ] }, { "diagram": "PGDP/printed/image/MathVR_40938_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "E", "C", "F" ], "lines": [ "line F E", "line D C", "line A D", "line B E C", "line D E", "line A F B" ], "circles": [], "semantics": [ "BC \\perp AB on B", "FE \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_55605_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "C", "G", "O", "B", "D", "A" ], "lines": [ "line A D", "line O H", "line G O", "line B H C", "line B G A", "line B O D", "line C D" ], "circles": [], "semantics": [ "OH \\perp BC on H", "GO \\perp BA on G" ] }, { "diagram": "PGDP/printed/image/MathVR_16704_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "O", "D", "F" ], "lines": [ "line A F", "line A O B", "line C A", "line C O", "line C D B", "line D O F" ], "circles": [ "\\odot O lieson C A F B" ], "semantics": [ "m \\angle AOC = m \\angle 4", "m \\angle AOF = m \\angle 3", "m \\angle OAC = m \\angle 2", "m \\angle OBD = m \\angle 1", "m \\angle COD = m \\angle 5" ] }, { "diagram": "PGDP/printed/image/MathVR_73961_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "B", "P", "C", "A", "D" ], "lines": [ "line P C", "line P B", "line D C", "line P Q", "line B Q C", "line A P D", "line A B" ], "circles": [], "semantics": [ "DC \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_56429_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "P", "C", "D" ], "lines": [ "line D C", "line A D", "line A P", "line P D", "line B C", "line A B", "line P C" ], "circles": [], "semantics": [ "CP = \\sqrt{3}", "DP = \\sqrt{2}", "AP = 1" ] }, { "diagram": "PGDP/printed/image/MathVR_39591_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B" ], "lines": [ "line D A", "line A B", "line C B", "line C D", "line C A" ], "circles": [], "semantics": [ "DA \\perp CD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_12215_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "C", "D", "B" ], "lines": [ "line C D", "line B E", "line B C", "line A E D", "line A B" ], "circles": [], "semantics": [ "BE \\perp AD on E", "m \\angle CDE = m \\angle \\beta", "m \\angle EAB = m \\angle \\alpha" ] }, { "diagram": "PGDP/printed/image/MathVR_73028_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "D" ], "lines": [ "line A D", "line B E C", "line D C", "line A C", "line A E", "line A B" ], "circles": [], "semantics": [ "AC \\perp AB on A", "m \\angle ECA = m \\angle 2", "m \\angle DAC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_45472_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "P", "D", "C", "O", "M", "N" ], "lines": [ "line B P", "line A C", "line P A", "line B D", "line M D P O C N" ], "circles": [ "\\odot O lieson M B A N" ], "semantics": [ "BD \\perp MN on D", "AC \\perp MN on C" ] }, { "diagram": "PGDP/printed/image/MathVR_66681_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "C", "A", "D" ], "lines": [ "line C A", "line D B A", "line E B", "line D C", "line E C", "line B C", "line D E" ], "circles": [], "semantics": [ "DC \\perp EC on C", "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_30005_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "O_{1}", "B", "E", "O" ], "lines": [ "line E C O_{1} O", "line D O_{1}", "line A O_{1}", "line E D A", "line A O B" ], "circles": [ "\\odot O_{1} lieson D C O", "\\odot O lieson A C B" ], "semantics": [ "EO \\perp AB on O" ] }, { "diagram": "PGDP/printed/image/MathVR_70684_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "D", "C", "B" ], "lines": [ "line B C", "line C D", "line A E D", "line B A", "line B E" ], "circles": [], "semantics": [ "CD \\perp AD on D", "AD \\perp BE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_72081_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "M", "O", "A", "B" ], "lines": [ "line C M D", "line A M O B" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [ "CD \\perp AB on M" ] }, { "diagram": "PGDP/printed/image/MathVR_40651_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "G", "A", "D", "E", "B", "O", "F" ], "lines": [ "line C F B", "line A E C", "line A G D B", "line C O D", "line E G" ], "circles": [ "\\odot O lieson E C F D" ], "semantics": [ "AB \\perp CD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_30076_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B" ], "lines": [ "line B C", "line B A", "line A C" ], "circles": [], "semantics": [ "m \\angle CBA = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_236_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "E", "B", "A", "C", "P", "N", "F", "D", "H" ], "lines": [ "line A F D", "line D C", "line B P F", "line F N H E", "line A N", "line B E C", "line P N", "line A P", "line A G B", "line G P H" ], "circles": [], "semantics": [ "PN \\perp AP on P" ] }, { "diagram": "PGDP/printed/image/MathVR_30276_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "C", "O", "A" ], "lines": [ "line A C", "line B O", "line O E", "line B E C", "line A B", "line O C" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "OE \\perp BC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_23078_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "D", "B", "A", "C" ], "lines": [ "line A B", "line E D C", "line B C", "line E A", "line D B", "line A D" ], "circles": [], "semantics": [ "BC \\perp DB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_82769_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "M", "N", "P" ], "lines": [ "line A P", "line A M B", "line M N", "line P N", "line B N", "line P M" ], "circles": [], "semantics": [ "BN \\perp BA on B" ] }, { "diagram": "PGDP/printed/image/MathVR_43477_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D" ], "lines": [ "line C D", "line C A", "line B D A", "line B C" ], "circles": [], "semantics": [ "CD \\perp BA on D", "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_44533_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "F", "E", "A", "D" ], "lines": [ "line B D E", "line B C F", "line A D C", "line A B", "line E C" ], "circles": [], "semantics": [ "m \\angle BDA = m \\angle 1", "m \\angle EDC = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_14855_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "A", "B", "O" ], "lines": [ "line O P", "line A P B", "line O B" ], "circles": [ "\\odot O lieson B A" ], "semantics": [ "OP \\perp AB on P" ] }, { "diagram": "PGDP/printed/image/MathVR_45080_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "C", "A", "F", "B", "D" ], "lines": [ "line E F", "line E D", "line D F", "line C F B", "line A D B", "line A E C" ], "circles": [], "semantics": [ "ED \\perp DF on D", "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_74534_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "A", "C", "F", "D" ], "lines": [ "line A D", "line E B F C", "line D C", "line B D", "line D F", "line E A", "line A B" ], "circles": [], "semantics": [ "EC \\perp DF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_42599_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "A", "C", "D" ], "lines": [ "line A D", "line B E C", "line A E", "line C D", "line B A" ], "circles": [], "semantics": [ "m \\angle EBA = 30", "AB = x" ] }, { "diagram": "PGDP/printed/image/MathVR_45598_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "B", "C", "D" ], "lines": [ "line B C", "line A E D C", "line B D", "line B E", "line B A" ], "circles": [], "semantics": [ "AC \\perp BE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_25005_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "E", "F" ], "lines": [ "line D C F", "line C A", "line A B", "line F B", "line A E F", "line C E B", "line D A" ], "circles": [], "semantics": [ "m \\angle BAE = m \\angle 1", "m \\angle CFE = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_46838_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "F", "G", "E", "D" ], "lines": [ "line E C", "line D G F C", "line A D", "line B C", "line E G", "line D E", "line A E B", "line E F" ], "circles": [], "semantics": [ "DC \\perp EG on G" ] }, { "diagram": "PGDP/printed/image/MathVR_2496_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "B", "C", "E", "F", "A" ], "lines": [ "line A F C", "line E P", "line A P", "line E F", "line B P C", "line B E A", "line P F" ], "circles": [], "semantics": [ "EP \\perp PF on P", "m \\angle FCP = m \\angle 4", "m \\angle EP = m \\angle 1", "m \\angle PAE = m \\angle 3", "m \\angle CPF = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_17165_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "E", "C", "P" ], "lines": [ "line A C", "line B P A", "line P D", "line B D E C", "line A E", "line A D" ], "circles": [], "semantics": [ "BC \\perp AE on E", "PD \\perp BC on D", "m \\angle EDA = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_63918_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "A", "C", "E", "D", "B" ], "lines": [ "line B D F", "line A F C", "line B E A", "line E D C" ], "circles": [], "semantics": [ "BA \\perp EC on E", "BF \\perp AC on F" ] }, { "diagram": "PGDP/printed/image/MathVR_15431_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "F", "B", "O" ], "lines": [ "line A O B", "line C D B", "line C F A", "line F D", "line D O", "line A D" ], "circles": [ "\\odot O lieson A D B" ], "semantics": [ "CA \\perp FD on F" ] }, { "diagram": "PGDP/printed/image/MathVR_12271_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "Q", "A", "B", "P", "M", "C", "H" ], "lines": [ "line C B", "line A M N H B", "line Q N", "line P M", "line C Q P A", "line Q B", "line C H" ], "circles": [], "semantics": [ "PM \\perp AB on M", "QN \\perp AB on N", "CH \\perp AB on H", "BC \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_75054_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "F", "A", "B", "O", "D" ], "lines": [ "line E C B", "line F A O B", "line F D E" ], "circles": [ "\\odot O lieson D A B C" ], "semantics": [ "EB \\perp FE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_44341_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "F", "B", "E" ], "lines": [ "line B C", "line A F B", "line F E", "line A E C", "line F C" ], "circles": [], "semantics": [ "AB \\perp FE on F" ] }, { "diagram": "PGDP/printed/image/MathVR_71592_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "M", "A", "B", "P'", "D", "C", "P" ], "lines": [ "line C P", "line C D A", "line C M B", "line P' D B", "line A E B", "line P' C", "line P' A", "line P' M P", "line P B", "line D E" ], "circles": [], "semantics": [ "AB \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_74009_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "C", "D", "O", "A" ], "lines": [ "line D O", "line A O C", "line B D A", "line B E C", "line D C", "line D E" ], "circles": [ "\\odot O lieson D A C" ], "semantics": [ "AC \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_31949_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "N", "M", "A", "Q" ], "lines": [ "line A B", "line N A C", "line B C M", "line N Q B", "line Q A M" ], "circles": [], "semantics": [ "m \\angle ANQ = m \\angle 1", "m \\angle ABQ = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_39319_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "B", "D", "E", "O", "C" ], "lines": [ "line A D F", "line A O E B", "line D B", "line F B", "line D E C", "line B C" ], "circles": [ "\\odot O lieson D A C B" ], "semantics": [ "AB \\perp DC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_3501_image1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "A" ], "lines": [ "line A C", "line B A", "line B D C", "line A D" ], "circles": [], "semantics": [ "BC \\perp AD on D", "m \\angle BAD = m \\angle 1", "m \\angle CAD = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_46819_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "E", "O", "A", "B" ], "lines": [ "line D E B", "line C B", "line D O", "line C E O", "line A D C", "line A O B" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "DO \\perp AC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_76382_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "Q", "P", "O", "A" ], "lines": [ "line C P Q", "line C O", "line A O P B", "line O Q" ], "circles": [ "\\odot O lieson A C B Q" ], "semantics": [ "m \\angle PQO = m \\angle \\alpha", "m \\angle PCO = m \\angle \\alpha", "m \\angle POQ = m \\angle \\alpha" ] }, { "diagram": "PGDP/printed/image/MathVR_47585_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "E", "C" ], "lines": [ "line A D", "line D C", "line B D", "line B E C", "line D E", "line A B" ], "circles": [], "semantics": [ "DC \\perp BD on D", "m \\angle DBE = m \\angle 1", "m \\angle DBA = m \\angle 2", "m \\angle ADB = m \\angle 3", "m \\angle CDE = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/MathVR_63765_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B" ], "lines": [ "line C B", "line A B", "line C D", "line A D" ], "circles": [], "semantics": [ "CB \\perp AB on B", "AB = 4", "BC=3", "AD = 13", "DC = 12" ] }, { "diagram": "PGDP/printed/image/MathVR_74988_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "P", "O", "C", "D" ], "lines": [ "line A P B", "line C O P D" ], "circles": [ "\\odot O lieson C A D B" ], "semantics": [ "AB \\perp CD on P" ] }, { "diagram": "PGDP/printed/image/MathVR_47306_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "A", "B", "C" ], "lines": [ "line A E", "line B D C", "line B E", "line E C", "line A C", "line A D", "line A B" ], "circles": [], "semantics": [ "BC \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_61943_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "E", "B" ], "lines": [ "line B C", "line A E B", "line E D", "line A D C" ], "circles": [], "semantics": [ "AB \\perp ED on E", "BC \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_52310_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "H", "C", "G", "B", "D", "F", "A" ], "lines": [ "line D F C", "line B G F", "line A E D", "line B H", "line E G C H", "line A B", "line B C" ], "circles": [], "semantics": [ "m \\angle GBC = m \\angle 2", "m \\angle FCG = m \\angle 3", "m \\angle BGC = m \\angle 4", "m \\angle CFG = m \\angle 5", "m \\angle HBC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_30539_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "F", "C", "M", "E", "N" ], "lines": [ "line A N C", "line B M A", "line B F C", "line A E F", "line M E N" ], "circles": [], "semantics": [ "BC \\perp AF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_67379_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line D C", "line A D", "line B C", "line A B" ], "circles": [], "semantics": [ "DC \\perp BC on C", "BA = 2", "DA = d", "DC = 3", "CB = 4" ] }, { "diagram": "PGDP/printed/image/MathVR_51445_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "E", "A" ], "lines": [ "line A C", "line E C", "line D A E", "line B C", "line D B", "line A B" ], "circles": [], "semantics": [ "EC \\perp DE on E", "DE \\perp DB on D", "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_79553_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "D", "C", "O", "F", "A" ], "lines": [ "line A F C", "line A D O B", "line A E", "line B E C", "line E F" ], "circles": [ "\\odot O lieson D E B" ], "semantics": [ "AC \\perp EF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_38390_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "A", "C", "D", "E", "B" ], "lines": [ "line D C", "line C B", "line A C", "line A F E B", "line C E", "line C F", "line D A" ], "circles": [], "semantics": [ "AB \\perp CE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_1092_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "B", "C", "A", "N", "E", "D" ], "lines": [ "line A D", "line D C", "line B N E D", "line A E", "line B F C", "line A N F", "line A B" ], "circles": [], "semantics": [ "BD \\perp AE on E", "BC \\perp AF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_12988_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "E", "F", "A" ], "lines": [ "line A F C", "line A E D", "line B E F", "line B D C", "line A B" ], "circles": [], "semantics": [ "m \\angle AEB = m \\angle e" ] }, { "diagram": "PGDP/printed/image/MathVR_48156_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "Q", "N", "P", "M" ], "lines": [ "line P A", "line O P", "line O A N", "line M Q O" ], "circles": [], "semantics": [ "PA \\perp ON on A" ] }, { "diagram": "PGDP/printed/image/MathVR_2360_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "N", "C", "E", "D" ], "lines": [ "line A D", "line O N C", "line D C", "line E N", "line D N", "line A E O" ], "circles": [], "semantics": [ "EN \\perp DN on N" ] }, { "diagram": "PGDP/printed/image/MathVR_69193_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "E", "C", "P", "A" ], "lines": [ "line A P C", "line E P", "line B P", "line B F C", "line P F", "line A E B" ], "circles": [], "semantics": [ "BC \\perp PF on F", "EP \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_71277_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "A", "M", "B", "N", "O", "D", "C" ], "lines": [ "line C B", "line M O H", "line D C", "line N H", "line A H B", "line D M N A", "line N O B" ], "circles": [], "semantics": [ "MH \\perp AB on H" ] }, { "diagram": "PGDP/printed/image/MathVR_9226_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "C", "A", "O", "D", "F" ], "lines": [ "line A D", "line D C", "line B O D", "line B E C", "line A O C", "line A B", "line F A E" ], "circles": [], "semantics": [ "BC \\perp FE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_7425_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "G", "B", "H", "C", "D", "M", "F", "E" ], "lines": [ "line A E C", "line E F", "line A D B", "line A M H", "line B G H F C", "line D G", "line D M E" ], "circles": [], "semantics": [ "AH \\perp BC on H" ] }, { "diagram": "PGDP/printed/image/MathVR_7307_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "O", "C", "E" ], "lines": [ "line C O E D", "line A E B" ], "circles": [ "\\odot O lieson C B D A" ], "semantics": [ "CD \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_37445_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "O", "B", "E", "D" ], "lines": [ "line D C E", "line A C", "line C B", "line C O", "line D A", "line A O B" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "m \\angle CAD = m \\angle 3", "m \\angle ACO = m \\angle 2", "m \\angle CAO = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_71676_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "M", "N" ], "lines": [ "line M C E B", "line E A", "line C D", "line N D G F A", "line B A", "line B F", "line E G", "line M N" ], "circles": [], "semantics": [ "NA \\perp EG on G", "NA \\perp BF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_78335_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "D" ], "lines": [ "line D C", "line C B", "line A D B", "line A C" ], "circles": [], "semantics": [ "CB \\perp AC on C", "CA = 12", "CB = 5" ] }, { "diagram": "PGDP/printed/image/MathVR_3691_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "O", "B", "A" ], "lines": [ "line O A", "line O B", "line C B A", "line O C" ], "circles": [], "semantics": [ "m \\angle OAB = 30", "m \\angle OBC = 45" ] }, { "diagram": "PGDP/printed/image/MathVR_53389_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "D", "A", "P" ], "lines": [ "line P C", "line E D", "line A D C", "line A E B", "line B P D", "line B C" ], "circles": [], "semantics": [ "ED \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_82009_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "E", "F", "P" ], "lines": [ "line A F C", "line A P", "line A E B", "line E F", "line E P", "line F P", "line B P C" ], "circles": [], "semantics": [ "EP \\perp PF on P", "m \\angle FCP = m \\angle 4", "m \\angle APE = m \\angle 1", "m \\angle PAE = m \\angle 3", "m \\angle CPF = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_21721_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "D", "E", "F", "N" ], "lines": [ "line F D E C", "line D A", "line D N", "line B F N", "line B E A", "line C A", "line B C", "line N A" ], "circles": [], "semantics": [ "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_219_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "C" ], "lines": [ "line C A", "line D C", "line C B", "line D A", "line B A" ], "circles": [], "semantics": [ "CB \\perp BA on B" ] }, { "diagram": "PGDP/printed/image/MathVR_72139_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "A", "C", "O", "D", "E" ], "lines": [ "line A F D", "line B E C", "line D C", "line B O D", "line F O E", "line A O C", "line A B" ], "circles": [], "semantics": [ "EF \\perp AC on O", "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_67386_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "A", "C", "D", "E" ], "lines": [ "line A D", "line E F D C", "line A E", "line B C", "line A F", "line A B", "line A C" ], "circles": [], "semantics": [ "EC \\perp AF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_31340_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "B", "O", "A" ], "lines": [ "line D A", "line C B", "line A O B", "line D C" ], "circles": [], "semantics": [ "CB \\perp DC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_37624_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "G", "O", "B", "A", "E", "C", "F" ], "lines": [ "line D E", "line C E B", "line D F G", "line A D C", "line D O", "line A O F B" ], "circles": [ "\\odot O lieson A D B G" ], "semantics": [ "DE \\perp CB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_75095_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "F", "A", "C", "D", "B" ], "lines": [ "line E C", "line D C", "line B C", "line A B F", "line A E D", "line A C", "line C F" ], "circles": [], "semantics": [ "EC \\perp AD on E", "AF \\perp CF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_48056_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "A", "C", "B", "M", "Q" ], "lines": [ "line M P", "line Q P", "line A P B", "line C M B", "line C Q A", "line Q M" ], "circles": [], "semantics": [ "MP \\perp QM on M", "AB \\perp CA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_13568_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "M", "B", "C", "D" ], "lines": [ "line A M B", "line C B", "line D B", "line C A", "line C D", "line C M" ], "circles": [], "semantics": [ "DB \\perp CD on D", "AB \\perp CM on M", "AB \\perp DB on B", "m \\angle ACM = m \\angle 1", "m \\angle BCM = m \\angle 2", "m \\angle AMC = m \\angle 4", "m \\angle BMC = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_37719_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "P", "E", "C", "F", "Q", "H", "A" ], "lines": [ "line A P H Q C", "line E Q", "line F E", "line B E C", "line P E", "line F P", "line A F B", "line E H" ], "circles": [], "semantics": [ "AC \\perp EH on H" ] }, { "diagram": "PGDP/printed/image/MathVR_31115_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C", "E" ], "lines": [ "line E D", "line A D", "line B D C", "line A E C", "line A B" ], "circles": [], "semantics": [ "BC \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_30582_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "H", "C", "F", "A", "E", "B" ], "lines": [ "line C H E", "line B E A", "line C B", "line C F", "line D F A", "line H F", "line C D", "line E F" ], "circles": [], "semantics": [ "CE \\perp HF on H" ] }, { "diagram": "PGDP/printed/image/MathVR_35522_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "E", "A" ], "lines": [ "line E C", "line A E", "line A D", "line D E", "line B D", "line B C", "line A C", "line A B" ], "circles": [], "semantics": [ "m \\angle DAB = m \\angle \\theta" ] }, { "diagram": "PGDP/printed/image/MathVR_64890_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "F", "D", "B", "A" ], "lines": [ "line A B", "line A C", "line F A", "line D C", "line E C", "line D A", "line F E", "line C B" ], "circles": [], "semantics": [ "m \\angle ABC = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_79259_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B", "O", "E" ], "lines": [ "line C B", "line A O C", "line O E", "line A E B", "line D O B", "line D A" ], "circles": [], "semantics": [ "OE \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_7743_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "O", "A" ], "lines": [ "line O C", "line O B", "line C B", "line O A", "line B A" ], "circles": [ "\\odot O lieson B C" ], "semantics": [ "m \\angle OBA = m \\angle 1", "m \\angle OBC = m \\angle 3", "m \\angle OCB = m \\angle 2", "m \\angle COB = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/MathVR_72132_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "D", "B", "C", "P", "G", "A", "E" ], "lines": [ "line P E G", "line A C", "line A E D", "line F E", "line P F", "line B F D G C", "line A P B" ], "circles": [], "semantics": [ "PG \\perp AB on P" ] }, { "diagram": "PGDP/printed/image/MathVR_72886_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "B", "A", "P", "C", "Q", "D" ], "lines": [ "line P Q", "line D Q C", "line A P D", "line P E", "line B F E C", "line P F", "line A B", "line E Q" ], "circles": [], "semantics": [ "PE \\perp EQ on E", "BC \\perp PF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_1204_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "M", "G", "N", "C" ], "lines": [ "line C N B", "line C G D", "line A D B", "line C M A", "line M G N" ], "circles": [], "semantics": [ "CB \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_73444_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "R'", "R", "H", "B", "A", "C", "O", "E", "P" ], "lines": [ "line B O", "line O H", "line Q R", "line A Q E", "line B R' P H R C", "line Q O P", "line A O C", "line A R'", "line A B" ], "circles": [], "semantics": [ "QR \\perp BC on R", "BC \\perp AR' on R'", "OB \\perp AC on O", "OH \\perp BC on H" ] }, { "diagram": "PGDP/printed/image/MathVR_55413_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "E", "F", "C" ], "lines": [ "line E D", "line C F B", "line A D B", "line A E C", "line F D" ], "circles": [], "semantics": [ "ED \\perp FD on D", "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_66391_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "M", "N", "P" ], "lines": [ "line A M D", "line F G", "line E M F", "line M N", "line B N C G", "line F D P C", "line M P G", "line A E B" ], "circles": [], "semantics": [ "MN \\perp BG on N" ] }, { "diagram": "PGDP/printed/image/MathVR_75738_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "A", "B", "G", "E", "F" ], "lines": [ "line G F", "line C G E", "line E F", "line C D F B", "line A E B", "line A G D", "line A C" ], "circles": [], "semantics": [ "m \\angle GEF = m \\angle 2", "m \\angle GCA = m \\angle 5", "m \\angle EGA = m \\angle 3", "m \\angle ACE = m \\angle 4", "m \\angle AEC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_15573_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "M", "N", "K" ], "lines": [ "line A B", "line B C", "line K C F D", "line A E D", "line B F N", "line B E M", "line E F", "line B K" ], "circles": [], "semantics": [ "KD \\perp BC on C", "AD \\perp BA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_8382_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "F", "D" ], "lines": [ "line E C", "line D C", "line F E", "line A E D", "line B C", "line A F B" ], "circles": [], "semantics": [ "m \\angle FEA = m \\angle 3", "m \\angle ECD = m \\angle 1", "m \\angle CED = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_61332_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B", "G", "F", "O" ], "lines": [ "line F D", "line D A", "line D O", "line C A", "line B D", "line G F B C", "line B O A" ], "circles": [ "\\odot O lieson B D A C" ], "semantics": [ "CA \\perp GC on C", "FD \\perp GC on F" ] }, { "diagram": "PGDP/printed/image/MathVR_20886_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "B'", "A", "E", "C", "O" ], "lines": [ "line B' C", "line B O B'", "line B D C", "line A O E C", "line A B", "line B' E D" ], "circles": [], "semantics": [ "BB' \\perp AC on O" ] }, { "diagram": "PGDP/printed/image/MathVR_64024_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D" ], "lines": [ "line B C", "line D B", "line A C", "line A D" ], "circles": [], "semantics": [ "BC \\perp DB on B", "AC \\perp AD on A" ] }, { "diagram": "PGDP/printed/image/MathVR_45858_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "C", "A", "E", "D" ], "lines": [ "line A D", "line E C F", "line B C", "line D C", "line B F", "line l lieson A E", "line A B", "line E H B" ], "circles": [], "semantics": [ "EF \\perp AE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_30704_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "E", "D" ], "lines": [ "line A E", "line D E C", "line D A", "line B C", "line A B" ], "circles": [], "semantics": [ "m \\angle EDA = m \\angle \\alpha" ] }, { "diagram": "PGDP/printed/image/MathVR_5044_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "P", "A" ], "lines": [ "line B P", "line C P A", "line B A", "line B C" ], "circles": [], "semantics": [ "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_45692_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "E", "C" ], "lines": [ "line B E C", "line A D C", "line D E", "line A B", "line D B" ], "circles": [], "semantics": [ "BC \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_32507_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "E", "F", "C" ], "lines": [ "line D C", "line C B", "line A E F C", "line D F", "line A B", "line D A", "line E B" ], "circles": [], "semantics": [ "m \\angle EAD = m \\angle 3", "m \\angle BCF = m \\angle 4", "m \\angle DCF = m \\angle 1", "m \\angle EAB = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_67736_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "D", "C", "A" ], "lines": [ "line D E", "line B A", "line A E", "line D A", "line B C", "line C A" ], "circles": [], "semantics": [ "BC \\perp CA on C", "AE \\perp DA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_9628_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "B", "C", "M", "D", "E", "A" ], "lines": [ "line A E C", "line P E", "line D P", "line B P C", "line A M D B", "line M C" ], "circles": [], "semantics": [ "DP \\perp AB on D", "AB \\perp MC on M", "AC \\perp PE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_71096_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "C", "D", "F" ], "lines": [ "line D C", "line A D", "line D F", "line B E C", "line A F E", "line A B" ], "circles": [], "semantics": [ "DF \\perp AE on F" ] }, { "diagram": "PGDP/printed/image/MathVR_54449_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "B", "C", "D", "F", "E", "A" ], "lines": [ "line A E C", "line A F G", "line B G C", "line A D B", "line D F E" ], "circles": [], "semantics": [ "AG \\perp DE on F", "AG \\perp BC on G" ] }, { "diagram": "PGDP/printed/image/MathVR_42916_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "G", "C", "A", "F", "E", "B", "O" ], "lines": [ "line C F B", "line D G B", "line D F O", "line D A", "line E C D", "line E A O B" ], "circles": [ "\\odot O lieson A C G B" ], "semantics": [ "DB \\perp ED on D" ] }, { "diagram": "PGDP/printed/image/MathVR_67201_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "M", "O", "A", "B" ], "lines": [ "line C M D", "line A O M B", "line O D" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [ "CD \\perp AB on M" ] }, { "diagram": "PGDP/printed/image/MathVR_55277_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "O", "C", "P", "A" ], "lines": [ "line A P", "line A C B", "line B P", "line O B", "line A O", "line O C P" ], "circles": [ "\\odot O lieson A B" ], "semantics": [ "AB \\perp OP on C" ] }, { "diagram": "PGDP/printed/image/MathVR_73745_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "O", "B", "D", "H", "C", "F", "G", "A", "M", "N" ], "lines": [ "line A C", "line E A G N D", "line H A", "line B M A", "line B O D C", "line E H F B", "line M G", "line F M N C" ], "circles": [ "\\odot O lieson B F A C" ], "semantics": [ "ED \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_65090_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "N", "B", "F", "C", "P", "M", "A", "D" ], "lines": [ "line A M D", "line D C", "line E M", "line F E", "line P N", "line B N C", "line P D", "line F A P B", "line D N" ], "circles": [], "semantics": [ "m \\angle PNB = m \\angle 3", "m \\angle NPB = m \\angle l", "m \\angle DPA = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_45712_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "A", "D", "B", "F", "G", "E", "C" ], "lines": [ "line C E B", "line C H", "line D C", "line A H F B", "line E F", "line D G A", "line G E" ], "circles": [], "semantics": [ "CH \\perp AB on H" ] }, { "diagram": "PGDP/printed/image/MathVR_64003_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "O" ], "lines": [ "line B O", "line A C", "line A O", "line B C", "line A B", "line O C" ], "circles": [], "semantics": [ "m \\angle BCO = m \\angle 2", "m \\angle OBC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_44311_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "B", "E", "C", "D" ], "lines": [ "line A E C", "line D C", "line A D", "line B F C", "line B A", "line F E D" ], "circles": [], "semantics": [ "AC \\perp BA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_74526_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "C", "B", "E", "D" ], "lines": [ "line C E F D", "line D B", "line E B", "line A B", "line F B", "line C B", "line C A" ], "circles": [], "semantics": [ "CD \\perp FB on F" ] }, { "diagram": "PGDP/printed/image/MathVR_75319_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "O", "F", "D", "E" ], "lines": [ "line A E F", "line A B", "line B D E", "line B O F", "line A D O" ], "circles": [], "semantics": [ "m \\angle DBO = m \\angle 2", "m \\angle ABD = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_67892_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "C", "D", "H", "A" ], "lines": [ "line B C", "line A E H C", "line E D", "line A D B", "line D H" ], "circles": [], "semantics": [ "BC \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_56127_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "F", "E", "O" ], "lines": [ "line A E C", "line A F B", "line B D C", "line A O", "line B O", "line C O", "line D O", "line E O", "line F O" ], "circles": [], "semantics": [ "OD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_29917_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "F", "E", "A", "D" ], "lines": [ "line A D", "line D C", "line B E D", "line A E", "line B F C", "line D F", "line B A" ], "circles": [], "semantics": [ "BD \\perp AE on E", "BC \\perp DF on F", "m \\angle EBA = m \\angle 1", "m \\angle ADE = m \\angle 3", "m \\angle EBF = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_2967_image2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "M", "N", "O" ], "lines": [ "line C N B", "line A O B", "line M O", "line N O", "line C M A" ], "circles": [ "\\odot O lieson M N" ], "semantics": [ "CB \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_65211_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "B", "C'" ], "lines": [ "line C' A", "line C A", "line B D A", "line B C'", "line B C", "line C' D C" ], "circles": [], "semantics": [ "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_38983_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "B", "E", "F", "G" ], "lines": [ "line C F G B", "line A E F", "line A D B", "line C E D", "line C A", "line E G" ], "circles": [], "semantics": [ "AB \\perp CD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_62007_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "B", "D", "A", "C", "E" ], "lines": [ "line A D", "line B F C", "line D C", "line B E D", "line A E", "line A F", "line A B" ], "circles": [], "semantics": [ "BC \\perp AF on F", "m \\angle EBA = m \\angle 1", "m \\angle ADE = m \\angle 3", "m \\angle FBE = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_15157_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "A'", "E" ], "lines": [ "line B D A'", "line A E", "line D E", "line C E A'", "line A D", "line B C" ], "circles": [], "semantics": [ "m \\angle BDA = m \\angle 1", "m \\angle AEC = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_3324_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "M", "N", "D" ], "lines": [ "line A D", "line M C", "line D C", "line B M N D", "line A N", "line A M", "line B C", "line N C", "line A B" ], "circles": [], "semantics": [ "BD \\perp AM on M", "BD \\perp NC on N" ] }, { "diagram": "PGDP/printed/image/MathVR_37339_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "D", "B", "O", "M", "C" ], "lines": [ "line D C", "line M O", "line O E", "line M E", "line A E B", "line C O B", "line D M A" ], "circles": [ "\\odot O lieson M C B E" ], "semantics": [ "m \\angle OEB = m \\angle 1", "m \\angle OBE = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_80117_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "P", "B", "A", "C", "E", "O", "M", "Q", "D" ], "lines": [ "line A Q", "line B F", "line D Q C", "line D O E B", "line A D", "line A M E F P", "line B P C", "line A O C", "line A B", "line P Q" ], "circles": [], "semantics": [ "BF \\perp AP on F" ] }, { "diagram": "PGDP/printed/image/MathVR_70897_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "F", "B", "D", "E", "C" ], "lines": [ "line F C B", "line D A", "line E A B", "line D F", "line D E", "line D C" ], "circles": [], "semantics": [ "EB \\perp DE on E", "FB \\perp DF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_244_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "G", "C", "E", "F", "A", "D" ], "lines": [ "line E F", "line E G", "line B D C", "line A F C", "line E D", "line G D F", "line B G", "line B E A" ], "circles": [], "semantics": [ "ED \\perp GF on D" ] }, { "diagram": "PGDP/printed/image/MathVR_9601_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "C" ], "lines": [ "line C B", "line C D", "line A D B", "line C A" ], "circles": [], "semantics": [ "m \\angle DAC = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_48298_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line D A", "line E D C", "line B E", "line C A", "line B A", "line B C" ], "circles": [], "semantics": [ "DA \\perp EC on D", "EC \\perp BE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_40202_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "C", "O", "D", "A" ], "lines": [ "line A E D C", "line B C", "line A O B", "line O E", "line D B", "line O D" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "AC \\perp OE on E", "m \\angle OBD = m \\angle 1", "m \\angle CBD = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_42592_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "B", "E", "D", "C", "G", "A", "F" ], "lines": [ "line A G C E", "line B H F C", "line D H", "line G F", "line D G", "line A D B", "line D F E" ], "circles": [], "semantics": [ "AE \\perp DG on G" ] }, { "diagram": "PGDP/printed/image/MathVR_32100_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B" ], "lines": [ "line B C", "line B A", "line D A", "line B D", "line C A" ], "circles": [], "semantics": [ "m \\angle ABD = m \\angle 1", "m \\angle BAD = m \\angle 3", "m \\angle CBA = m \\angle 2", "m \\angle BAC = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/MathVR_16103_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A D", "line C E D", "line A C", "line B D", "line A B", "line A E" ], "circles": [], "semantics": [ "m \\angle DAE = 30", "m \\angle CAE = 45" ] }, { "diagram": "PGDP/printed/image/MathVR_77983_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C", "O" ], "lines": [ "line D C", "line D O B", "line A D", "line B C", "line A O C", "line A B" ], "circles": [], "semantics": [ "AD = 3" ] }, { "diagram": "PGDP/printed/image/MathVR_41489_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "M", "A", "D", "B", "E", "C", "H" ], "lines": [ "line D F C", "line A M H B", "line C B", "line E H", "line F E M", "line D E B", "line D M", "line D A" ], "circles": [], "semantics": [ "m \\angle HME = m \\angle 4", "m \\angle EMD = m \\angle 3", "m \\angle MDA = m \\angle 2", "m \\angle MAD = m \\angle 1", "m \\angle HBE = m \\angle 5" ] }, { "diagram": "PGDP/printed/image/MathVR_27140_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C" ], "lines": [ "line B C", "line A C", "line A B" ], "circles": [], "semantics": [ "BC = 6", "BA = 4" ] }, { "diagram": "PGDP/printed/image/MathVR_51558_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "G", "B", "M", "F", "E", "C" ], "lines": [ "line C G E B", "line C F D", "line F G", "line A F E", "line A D M B", "line E M", "line A C", "line F B" ], "circles": [], "semantics": [ "CB \\perp AC on C", "CD \\perp AB on D" ] }, { "diagram": "PGDP/printed/image/MathVR_40598_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B" ], "lines": [ "line D C", "line C B", "line C A", "line A B", "line D A" ], "circles": [], "semantics": [ "DC \\perp DA on D", "CB \\perp CA on C", "m \\angle DCA = m \\angle 1", "m \\angle CAD = m \\angle 3", "m \\angle CAB = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_22467_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B", "P" ], "lines": [ "line D C", "line A P B", "line C B", "line C P", "line D P", "line D A" ], "circles": [], "semantics": [ "m \\angle PBC = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_62088_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "P", "D", "M", "B" ], "lines": [ "line A M B", "line M P", "line A P", "line A D C", "line P D" ], "circles": [], "semantics": [ "AC \\perp PD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_32379_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "E", "B", "O" ], "lines": [ "line A B", "line D A", "line D C", "line C E B", "line A E", "line A O C", "line D O B" ], "circles": [], "semantics": [ "CB \\perp AE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_10463_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "A", "E", "B", "D", "C", "F" ], "lines": [ "line P B D C", "line A F C", "line P E", "line A D", "line A B E", "line P F" ], "circles": [], "semantics": [ "PC \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_3587_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "H", "D", "C", "F", "E", "P", "A", "Q" ], "lines": [ "line A E D", "line P Q", "line E C", "line E F", "line B F H Q C", "line D C", "line P E", "line A H", "line A P B" ], "circles": [], "semantics": [ "BC \\perp AH on H" ] }, { "diagram": "PGDP/printed/image/MathVR_34448_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "G", "G'", "D", "F" ], "lines": [ "line A G' D", "line F D C", "line A E", "line B E C", "line A F", "line A G B" ], "circles": [], "semantics": [ "m \\angle EAG = m \\angle G'AH" ] }, { "diagram": "PGDP/printed/image/MathVR_8416_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "B", "O", "D", "A", "C" ], "lines": [ "line E B", "line E F", "line C B", "line E O", "line E D", "line A E C", "line A D F O B" ], "circles": [ "\\odot O lieson D E B" ], "semantics": [ "CB \\perp AC on C", "EB \\perp ED on E" ] }, { "diagram": "PGDP/printed/image/MathVR_30699_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "E", "O", "A", "B" ], "lines": [ "line C D B", "line D O", "line C E A", "line D A", "line D E", "line A O B" ], "circles": [ "\\odot O lieson A D B" ], "semantics": [ "CA \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_1858_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "D", "A", "M", "O", "B", "F", "E", "P", "C" ], "lines": [ "line O C", "line A M B P", "line D N C P", "line O B", "line O N", "line E O F P", "line M O" ], "circles": [ "\\odot O lieson E A B F C D" ], "semantics": [ "m \\angle CPF = m \\angle 2", "m \\angle BPF = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_61709_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B" ], "lines": [ "line C A", "line D A B", "line C B", "line C D" ], "circles": [], "semantics": [ "DB \\perp CD on D", "m \\angle CAB = m \\angle 1", "m \\angle CAD = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_43644_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "Q", "N", "P", "M", "D" ], "lines": [ "line A Q D", "line P C N", "line M N", "line D C", "line B C", "line M Q P", "line A P B" ], "circles": [], "semantics": [ "PN \\perp MP on P" ] }, { "diagram": "PGDP/printed/image/MathVR_63802_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "F", "B", "D" ], "lines": [ "line A D", "line A F E", "line B E", "line B A", "line B F D", "line D E" ], "circles": [], "semantics": [ "m \\angle FED = m \\angle 4", "m \\angle ABF = m \\angle 1", "m \\angle DAF = m \\angle 3", "m \\angle EBF = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_41605_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A" ], "lines": [ "line A B", "line C A", "line C B" ], "circles": [], "semantics": [ "AB \\perp CB on B", "AC = l", "BA = h", "m \\angle ACB = m \\angle \\theta" ] }, { "diagram": "PGDP/printed/image/MathVR_37863_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "F", "D", "C", "A", "P", "O", "B" ], "lines": [ "line C B", "line E D B", "line C O", "line P F", "line D O F", "line P C E", "line P A O B" ], "circles": [ "\\odot O lieson A C D B F" ], "semantics": [ "EB \\perp PE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_54761_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "C", "F", "D" ], "lines": [ "line A F C", "line B E A", "line E D", "line B D C", "line F D" ], "circles": [], "semantics": [ "m \\angle CDF = m \\angle 4", "m \\angle EDB = m \\angle 2", "m \\angle CFD = m \\angle 3", "m \\angle BED = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_15530_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "C", "E" ], "lines": [ "line B E A", "line C A", "line B D C", "line D E", "line E C" ], "circles": [], "semantics": [ "BC \\perp DE on D" ] }, { "diagram": "PGDP/printed/image/MathVR_56556_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "F", "P", "C", "Q", "U", "V", "D", "E" ], "lines": [ "line A P V", "line D V C", "line A E D", "line B Q V", "line U Q C", "line B F C", "line U P D", "line Q F", "line A U B", "line U V", "line E P" ], "circles": [], "semantics": [ "BC \\perp QF on F", "AD \\perp EP on E" ] }, { "diagram": "PGDP/printed/image/MathVR_66029_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "O", "C", "D", "A" ], "lines": [ "line A C B", "line O C D", "line B D", "line A O" ], "circles": [ "\\odot O lieson A B" ], "semantics": [ "OD \\perp AO on O" ] }, { "diagram": "PGDP/printed/image/MathVR_45364_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "D", "G", "C", "E", "H", "F" ], "lines": [ "line B F C", "line F H", "line A G B", "line E F", "line G E", "line A E", "line A D H C", "line B E D" ], "circles": [], "semantics": [ "BC \\perp AB on B", "AC \\perp BD on D", "AB \\perp GE on G" ] }, { "diagram": "PGDP/printed/image/MathVR_42323_img4.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "P", "C'", "E", "C", "B", "D" ], "lines": [ "line D B E", "line C' P D", "line C P", "line C' E", "line C A C'", "line A P B" ], "circles": [], "semantics": [ "CC' \\perp AB on A", "DE \\perp AB on B", "DE \\perp C'E on E" ] }, { "diagram": "PGDP/printed/image/MathVR_67160_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "B", "D", "A", "N", "C", "E" ], "lines": [ "line N E", "line D E C", "line l lieson N M", "line A N D", "line B C", "line A E", "line A M B" ], "circles": [], "semantics": [ "m \\angle EAM = m \\angle 3", "m \\angle NMA = m \\angle 2", "m \\angle NAE = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_39950_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "M", "D" ], "lines": [ "line M C", "line D C", "line A D", "line B C", "line D M", "line A M B" ], "circles": [], "semantics": [ "BC \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_67248_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "P", "B", "O", "C", "E" ], "lines": [ "line A C", "line A B D", "line A O E P", "line D P", "line B O", "line B E C" ], "circles": [ "\\odot O lieson A C P B" ], "semantics": [ "m \\angle CAO = m \\angle 2", "m \\angle BAO = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_52970_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "D", "C", "A", "O" ], "lines": [ "line C D", "line B O A", "line E D A", "line E C", "line C B", "line C A" ], "circles": [ "\\odot O lieson B C D A" ], "semantics": [ "EA \\perp EC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_15585_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "E", "C" ], "lines": [ "line C B", "line A E C", "line D C", "line D E", "line A B", "line D B", "line D A" ], "circles": [], "semantics": [ "AC \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_30606_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "C", "A", "D" ], "lines": [ "line D E", "line A E C", "line A D", "line B D", "line B C" ], "circles": [], "semantics": [ "m \\angle EDA = 45" ] }, { "diagram": "PGDP/printed/image/MathVR_45341_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B" ], "lines": [ "line D C", "line C B", "line A C", "line A B", "line D A" ], "circles": [], "semantics": [ "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_72146_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "B", "Q", "D", "P", "C" ], "lines": [ "line C D", "line A P", "line C P E", "line B C", "line A E Q D", "line P Q", "line B A" ], "circles": [], "semantics": [ "AD \\perp BA on A", "CE \\perp AD on E" ] }, { "diagram": "PGDP/printed/image/MathVR_70705_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B" ], "lines": [ "line C B", "line A B", "line A C" ], "circles": [], "semantics": [ "AC = 6", "CB = 8" ] }, { "diagram": "PGDP/printed/image/MathVR_9073_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "A" ], "lines": [ "line A C", "line A D", "line B D C", "line A B" ], "circles": [], "semantics": [ "AC = 3", "BA = 3", "CD = 2", "BD = 2" ] }, { "diagram": "PGDP/printed/image/MathVR_45980_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "M", "B", "N", "E", "C", "P", "D" ], "lines": [ "line A N D C", "line D M", "line A E B", "line E N", "line B P D", "line B M C", "line E P C" ], "circles": [], "semantics": [ "AC \\perp EN on N", "DM \\perp BC on M" ] }, { "diagram": "PGDP/printed/image/MathVR_75933_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "E", "M", "A", "N" ], "lines": [ "line E N C", "line B M", "line A C", "line A M N D", "line B N", "line B D C", "line E M", "line A E B" ], "circles": [], "semantics": [ "AD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_68503_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "M" ], "lines": [ "line A B", "line A E D", "line D C", "line B M F C", "line E M", "line E F" ], "circles": [], "semantics": [ "m \\angle FEM = m \\angle \\alpha", "AB = 60", "BC = 80" ] }, { "diagram": "PGDP/printed/image/MathVR_64135_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "D", "O", "A", "B" ], "lines": [ "line A O", "line B O D", "line A B", "line E O", "line C O", "line C D", "line A E C" ], "circles": [], "semantics": [ "EO \\perp AC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_41520_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B", "E", "F" ], "lines": [ "line C B", "line A C", "line D C", "line A F E B", "line C E", "line C F", "line D A" ], "circles": [], "semantics": [ "m \\angle CAF = m \\angle 2", "m \\angle CAD = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_66054_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "F", "C", "E" ], "lines": [ "line A D", "line B F C E", "line D E", "line A C", "line D C", "line A E", "line A F", "line A B" ], "circles": [], "semantics": [ "BE \\perp AF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_6142_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "Q", "E", "P", "B", "A", "O" ], "lines": [ "line Q O B", "line P A Q", "line A E", "line P E B", "line A B" ], "circles": [ "\\odot O lieson A B" ], "semantics": [ "AE \\perp PB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_4051_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "D", "E", "C", "A" ], "lines": [ "line B C", "line A B", "line D F E C", "line B E", "line A F", "line A D" ], "circles": [], "semantics": [ "DC \\perp BE on E", "DC \\perp AF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_71810_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "A", "D", "B", "F", "C", "E" ], "lines": [ "line D C", "line A E B", "line C B", "line A F C", "line D F E P", "line D A" ], "circles": [], "semantics": [ "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_38422_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "O", "A" ], "lines": [ "line A C", "line O B", "line O D", "line B D C", "line A B", "line O C" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "OD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_55931_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "E", "A" ], "lines": [ "line A D C", "line E C", "line B D E", "line B C", "line B A" ], "circles": [], "semantics": [ "EC \\perp BE on E", "AC \\perp BA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_67736_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "C", "B", "A", "D" ], "lines": [ "line D A", "line C E A", "line B A", "line B C", "line E D" ], "circles": [], "semantics": [ "CA \\perp BC on C", "DA \\perp CA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_45227_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "N", "E", "M", "O", "B", "C" ], "lines": [ "line A E N B", "line N O", "line O B", "line C E M D", "line M O" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [ "AB \\perp CD on E" ] }, { "diagram": "PGDP/printed/image/MathVR_45990_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "F", "M", "E", "O", "A", "B" ], "lines": [ "line C B", "line C E D", "line D B", "line C F M", "line A E O F B" ], "circles": [ "\\odot O lieson A C B M D" ], "semantics": [ "CM \\perp AB on F" ] }, { "diagram": "PGDP/printed/image/MathVR_70263_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "F", "H", "B", "E", "D", "N", "C", "A" ], "lines": [ "line B A", "line A H", "line B F H E C N", "line D A E", "line A F", "line M D B", "line A C" ], "circles": [], "semantics": [ "AH \\perp BN on H" ] }, { "diagram": "PGDP/printed/image/MathVR_43545_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "B", "O", "N", "F", "C" ], "lines": [ "line O C", "line O N", "line O F", "line B N C", "line A F C", "line A E B" ], "circles": [ "\\odot O lieson E F N" ], "semantics": [ "BC \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_29899_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G", "H", "P" ], "lines": [ "line D F C", "line A G", "line A D", "line B P", "line B G C", "line H P", "line C P", "line A H E B", "line E P F" ], "circles": [], "semantics": [ "HP \\perp AB on H", "AG \\perp BC on G" ] }, { "diagram": "PGDP/printed/image/MathVR_5918_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "M", "C", "B", "O" ], "lines": [ "line O D B", "line A C O", "line A B", "line A M" ], "circles": [], "semantics": [ "OB \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_33237_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "N" ], "lines": [ "line A N D", "line N B", "line E D C", "line B F E", "line N E", "line B C", "line A B", "line N F C" ], "circles": [], "semantics": [ "m \\angle DCF = m \\angle 2", "m \\angle CND = m \\angle 3", "m \\angle BCF = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_3358_image2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "O", "F", "A", "C", "E" ], "lines": [ "line E C", "line E F D", "line O D", "line A D", "line E B", "line A B F O C", "line D C" ], "circles": [ "\\odot O lieson B E C D" ], "semantics": [ "ED \\perp AC on F" ] }, { "diagram": "PGDP/printed/image/MathVR_14696_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F" ], "lines": [ "line A B", "line D C", "line C F", "line l lieson E B F", "line D A", "line A E", "line C B" ], "circles": [], "semantics": [ "EF \\perp AE on E", "CF \\perp EF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_30357_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "M", "B", "N", "E", "C", "A", "Q", "P", "D" ], "lines": [ "line E F", "line F D C", "line B M N C", "line A P Q D", "line E P", "line D N", "line A M", "line F Q", "line B A E" ], "circles": [], "semantics": [ "BC \\perp AM on M", "BC \\perp DN on N" ] }, { "diagram": "PGDP/printed/image/MathVR_36848_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "C", "A", "B", "H", "D" ], "lines": [ "line C H D", "line A H E", "line C E B", "line A D B", "line A C" ], "circles": [], "semantics": [ "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_62558_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "O", "D" ], "lines": [ "line O B", "line D C", "line O E", "line A D", "line B E C", "line A B", "line O C" ], "circles": [ "\\odot O lieson A D C B" ], "semantics": [ "OE \\perp BC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_35287_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "P" ], "lines": [ "line P A", "line B A", "line P B" ], "circles": [], "semantics": [ "BA=2", "PA=\\sqrt{3}", "PB=\\sqrt{3}" ] }, { "diagram": "PGDP/printed/image/MathVR_45486_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "E", "A", "B" ], "lines": [ "line A B", "line A D", "line A C", "line E A", "line D B", "line E D", "line C B" ], "circles": [], "semantics": [ "AC \\perp CB on C", "EA \\perp ED on E" ] }, { "diagram": "PGDP/printed/image/MathVR_86326_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "B", "A", "F", "C", "O", "E", "D" ], "lines": [ "line D C", "line B G O D", "line A D", "line E G", "line B C", "line A F O C", "line E O", "line F E", "line A E B" ], "circles": [], "semantics": [ "BD \\perp EG on G", "AC \\perp FE on F" ] }, { "diagram": "PGDP/printed/image/MathVR_51138_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "D", "B", "C", "E", "Q", "A", "O" ], "lines": [ "line A Q C", "line A O D", "line P O Q", "line B P D E C", "line Q E", "line A B", "line D Q" ], "circles": [], "semantics": [ "BC \\perp QE on E", "AD \\perp BC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_8425_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "K", "H", "P", "O" ], "lines": [ "line A O H B", "line A K", "line K P", "line P H" ], "circles": [ "\\odot O lieson A P B" ], "semantics": [ "PH \\perp AB on H", "KP \\perp KA on K" ] }, { "diagram": "PGDP/printed/image/MathVR_79509_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "C", "D", "B", "H", "E", "G", "A" ], "lines": [ "line E F", "line A B", "line D A", "line G E", "line F H", "line G F", "line C F B", "line D G C" ], "circles": [], "semantics": [ "m \\angle EFH = m \\angle 2", "m \\angle HFB = m \\angle 4", "m \\angle GFC = m \\angle 3", "m \\angle EFG = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_7187_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "D" ], "lines": [ "line D C", "line A D", "line B C", "line D E", "line A E B", "line E C" ], "circles": [], "semantics": [ "BC \\perp AB on B", "AD \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_52830_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "H", "C", "D", "B", "A", "F", "G", "E", "O" ], "lines": [ "line H C G B", "line D O", "line O G", "line F D H E", "line A O B", "line D B" ], "circles": [ "\\odot O lieson A D C B" ], "semantics": [ "HB \\perp FE on H" ] }, { "diagram": "PGDP/printed/image/MathVR_17724_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "B", "F", "A", "D" ], "lines": [ "line C A", "line B D C", "line F C", "line F D E", "line B E A", "line C E", "line F B" ], "circles": [], "semantics": [ "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_37753_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "D", "E", "C", "A", "G" ], "lines": [ "line D C", "line F G C", "line B C", "line A E D F", "line A B", "line A G", "line E B" ], "circles": [], "semantics": [ "AB \\perp AF on A" ] }, { "diagram": "PGDP/printed/image/MathVR_21567_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "C", "A", "B", "H", "D" ], "lines": [ "line C H D", "line A H E", "line C E B", "line A D B", "line A C" ], "circles": [], "semantics": [ "CD \\perp AE on H" ] }, { "diagram": "PGDP/printed/image/MathVR_73028_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line A D", "line B C", "line D C", "line A C", "line A B" ], "circles": [], "semantics": [ "AC \\perp AB on A", "m \\angle BCA = m \\angle 2", "m \\angle DAC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_48968_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "C", "A", "E", "B", "D", "H" ], "lines": [ "line B A", "line C P E D", "line A D", "line B H", "line A E", "line A H P", "line B P", "line B C" ], "circles": [], "semantics": [ "BH \\perp AP on H" ] }, { "diagram": "PGDP/printed/image/MathVR_70604_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "M", "D", "C" ], "lines": [ "line D M", "line C M B", "line D C", "line E M", "line A M", "line A B", "line D E A" ], "circles": [], "semantics": [ "m \\angle MDC = m \\angle 2", "m \\angle MDE = m \\angle 1", "m \\angle MAB = m \\angle 4", "m \\angle MAE = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_15509_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "D", "B", "F", "C" ], "lines": [ "line C B", "line F C", "line D C", "line F E", "line A E B", "line D F A", "line C E" ], "circles": [], "semantics": [ "FC \\perp FE on F" ] }, { "diagram": "PGDP/printed/image/MathVR_41730_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "B", "C", "N", "E", "A" ], "lines": [ "line A E C", "line N M", "line A N", "line B N E", "line B M C", "line A B" ], "circles": [], "semantics": [ "AN \\perp BE on N" ] }, { "diagram": "PGDP/printed/image/MathVR_73318_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "D", "O", "C" ], "lines": [ "line C D E B", "line A B", "line D O A", "line O E" ], "circles": [ "\\odot O lieson C B" ], "semantics": [ "OE \\\\perp CB on E", "AO = 8", "BA = 12" ] }, { "diagram": "PGDP/printed/image/MathVR_43745_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "D", "A" ], "lines": [ "line B D A", "line C D", "line B C", "line C E A" ], "circles": [ "\\odot C lieson B D E" ], "semantics": [ "BC \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_15341_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "E", "M", "F", "C" ], "lines": [ "line M D", "line C F B", "line A M E C", "line E D", "line A D B", "line F D" ], "circles": [], "semantics": [ "MD \\perp AC on M" ] }, { "diagram": "PGDP/printed/image/MathVR_64712_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "F", "B", "G", "A", "C", "D" ], "lines": [ "line A E", "line E C", "line A F", "line D G E", "line B F C", "line G C", "line F G", "line A C", "line A B", "line D C" ], "circles": [], "semantics": [ "EC \\perp BC on C", "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_62927_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "E", "A" ], "lines": [ "line B E", "line A C", "line A E D", "line B D C", "line A B", "line E C" ], "circles": [], "semantics": [ "m \\angle ACE = m \\angle 2", "m \\angle DCE = m \\angle 4", "m \\angle EBD = m \\angle 3", "m \\angle EBA = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_12671_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "O" ], "lines": [ "line A O", "line O D", "line A D B", "line O B" ], "circles": [ "\\odot O lieson B A" ], "semantics": [ "OD \\perp AB on D", "m \\angle AOD = m \\angle 1", "m \\angle DOB = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_5076_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B" ], "lines": [ "line B C", "line A B", "line A C" ], "circles": [], "semantics": [ "m \\angle BAC = m \\angle \\alpha" ] }, { "diagram": "PGDP/printed/image/MathVR_59484_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line A B", "line B C" ], "circles": [], "semantics": [ "BC = 10", "m \\angle ABC = 60", "m \\angle CAB = 45" ] }, { "diagram": "PGDP/printed/image/MathVR_3136_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "C", "B", "A", "E", "D" ], "lines": [ "line B A", "line C E", "line B E D F", "line C D A", "line B C", "line E A", "line F A" ], "circles": [], "semantics": [ "CE \\perp BF on E" ] }, { "diagram": "PGDP/printed/image/MathVR_46382_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "D", "F", "C", "E", "A", "B" ], "lines": [ "line A E", "line B E C", "line A G", "line A B", "line F E", "line D E", "line D G C", "line A F D" ], "circles": [], "semantics": [ "AG \\perp DC on G" ] }, { "diagram": "PGDP/printed/image/MathVR_38448_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "F", "P", "C", "D", "A", "O" ], "lines": [ "line D P F", "line A F C", "line B P", "line P E", "line B E C", "line A D B", "line P C" ], "circles": [ "\\odot O lieson D F E" ], "semantics": [ "DF \\perp PE on P" ] }, { "diagram": "PGDP/printed/image/MathVR_77579_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "B", "C" ], "lines": [ "line A B", "line C B", "line A C D", "line D B" ], "circles": [], "semantics": [ "AD \\perp DB on D", "BC = a", "AC = b", "BA = c" ] }, { "diagram": "PGDP/printed/image/MathVR_56638_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C" ], "lines": [ "line C D", "line A C", "line A B D", "line C B" ], "circles": [], "semantics": [ "m \\angle DBC = 60", "m \\angle CAB = 30" ] }, { "diagram": "PGDP/printed/image/MathVR_53353_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "E", "B", "F", "G", "D" ], "lines": [ "line C D B", "line A G C", "line G E", "line A D", "line A E B", "line C E", "line G D", "line G F", "line D F E" ], "circles": [], "semantics": [ "CB \\perp AD on D", "AB \\perp CE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_3056_image3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "M", "D", "B", "F", "O", "A", "C", "E" ], "lines": [ "line D C", "line E C", "line D E", "line P M", "line E F M", "line B E", "line A D", "line A B O F C", "line P C", "line D B" ], "circles": [ "\\odot O lieson B D E C M P" ], "semantics": [ "EM \\perp AC on F" ] }, { "diagram": "PGDP/printed/image/MathVR_57123_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C", "Q", "E", "P" ], "lines": [ "line E D", "line P D", "line B D C", "line Q D", "line A E Q C", "line A P B" ], "circles": [], "semantics": [ "PD \\perp QD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_76625_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "F", "D", "A", "B", "C" ], "lines": [ "line D B A", "line C A", "line F C B", "line F E A", "line D C E", "line D F" ], "circles": [], "semantics": [ "DA \\perp FB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_25220_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "O", "C", "B" ], "lines": [ "line A D B", "line C D O", "line O B" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "AB \\perp CO on D" ] }, { "diagram": "PGDP/printed/image/MathVR_23355_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "E", "A", "C", "F" ], "lines": [ "line D C", "line B F D", "line A D", "line A F", "line B E C", "line D E", "line A B" ], "circles": [], "semantics": [ "BD \\perp AF on F", "BC \\perp DE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_31828_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D" ], "lines": [ "line C A", "line B D A", "line B C" ], "circles": [ "\\odot D lieson A" ], "semantics": [ "CA \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_2076_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line A D", "line B C", "line A C", "line A B", "line C D" ], "circles": [], "semantics": [ "m \\angle DAC = m \\angle 2", "m \\angle CAB = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_75171_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "P", "A" ], "lines": [ "line A C", "line P C", "line A D", "line B D", "line B C", "line B P", "line A B", "line D C", "line D P" ], "circles": [], "semantics": [ "m \\angle ACD = m \\angle 2", "m \\angle CAD = m \\angle 1", "m \\angle DBC = m \\angle 4", "m \\angle DBP = m \\angle 5", "m \\angle BCD = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_5308_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "O", "C", "D", "B", "A" ], "lines": [ "line B C", "line A D", "line E B O A", "line E C D", "line O C", "line A C" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "m \\angle OCA = m \\angle 1", "m \\angle BCO = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_44388_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "D", "C" ], "lines": [ "line A D", "line B E C", "line E D", "line B A", "line C D", "line A E" ], "circles": [], "semantics": [ "m \\angle DAE = m \\angle 2", "m \\angle BEA = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_44234_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "C", "D", "B" ], "lines": [ "line A E C", "line B C", "line A D B", "line D E", "line B E" ], "circles": [], "semantics": [ "AC \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_20769_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "B", "A", "C", "F", "H", "D", "E" ], "lines": [ "line D H C", "line D B", "line A E D", "line E H", "line F G", "line B G C", "line E F", "line A F B", "line G H" ], "circles": [], "semantics": [ "BC \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_40623_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "D", "A" ], "lines": [ "line C D", "line A D", "line B A", "line B C" ], "circles": [], "semantics": [ "m \\angle ABC = 120" ] }, { "diagram": "PGDP/printed/image/MathVR_44090_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line G A E B", "line G F C", "line B C", "line C D", "line A F D", "line E F", "line E C" ], "circles": [], "semantics": [ "EC \\perp GB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_6347_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "B", "E", "F", "C", "N", "M" ], "lines": [ "line C E A", "line C O", "line N E O", "line A O B", "line N M", "line E F", "line C F B", "line M F O" ], "circles": [], "semantics": [ "CA \\perp CB on C", "NO \\perp MO on O" ] }, { "diagram": "PGDP/printed/image/MathVR_75363_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "A", "E", "M", "B", "D", "P" ], "lines": [ "line P B", "line M P", "line F P", "line F M A", "line A P", "line A E B", "line F D E", "line D P", "line P E" ], "circles": [], "semantics": [ "MP \\perp FA on M", "m \\angle PAE = m \\angle 2", "m \\angle MAP = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_74472_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "F", "C", "E" ], "lines": [ "line D F C", "line A E B", "line C B", "line D E", "line F B", "line D A" ], "circles": [], "semantics": [ "m \\angle FDE = m \\angle 2", "m \\angle AED = m \\angle 3", "m \\angle EBF = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_75186_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "G", "F", "A", "E" ], "lines": [ "line A F C", "line B A", "line B E F", "line B D C", "line A G E D", "line G F" ], "circles": [], "semantics": [ "AD \\perp GF on G" ] }, { "diagram": "PGDP/printed/image/MathVR_16030_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "B", "C", "E", "A", "D" ], "lines": [ "line D C", "line B E", "line A E D", "line B F C", "line E C", "line E F", "line A B" ], "circles": [], "semantics": [ "m \\angle DCE = m \\angle 4", "m \\angle EBA = m \\angle 1", "m \\angle EBF = m \\angle 2", "m \\angle FCE = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_23202_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line B D", "line B C", "line A D C", "line A B" ], "circles": [], "semantics": [ "BD \\perp AC on D" ] }, { "diagram": "PGDP/printed/image/MathVR_31961_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "O", "C", "E", "P", "F" ], "lines": [ "line A C F", "line A D O", "line D C", "line D E", "line E C", "line B E P F", "line C P", "line A B", "line B O C" ], "circles": [], "semantics": [ "BF \\perp CP on P" ] }, { "diagram": "PGDP/printed/image/MathVR_45156_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "B", "A", "N", "M", "C", "F" ], "lines": [ "line A F N", "line A E", "line A D", "line M E", "line B E C N", "line D F C", "line F E", "line A M B" ], "circles": [], "semantics": [ "ME \\perp AB on M", "AN \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_50601_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "C", "D", "B", "F" ], "lines": [ "line D C", "line A E B", "line C B", "line C F", "line E F", "line D F B", "line D E", "line D A" ], "circles": [], "semantics": [ "m \\angle EDA = m \\angle 1", "m \\angle CDF = m \\angle 2", "m \\angle FDE = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_40337_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "B", "E", "F", "C", "O", "A", "M" ], "lines": [ "line O M", "line A C", "line B G E C", "line A M E", "line B M", "line A F O B" ], "circles": [ "\\odot O lieson F M G B" ], "semantics": [ "m \\angle OMB = m \\angle 3", "m \\angle MBO = m \\angle 1", "m \\angle GBM = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_13386_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "A" ], "lines": [ "line A C", "line A D", "line B D C", "line A B" ], "circles": [], "semantics": [ "AB = 7", "AC = 7", "BC = 6" ] }, { "diagram": "PGDP/printed/image/MathVR_39821_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "B", "O", "C", "H", "G", "D", "A" ], "lines": [ "line H O", "line F O", "line O G", "line B D O", "line B E C G", "line O E", "line D C", "line F H A B", "line A D" ], "circles": [], "semantics": [ "HO \\perp FB on H", "OG \\perp BG on G" ] }, { "diagram": "PGDP/printed/image/MathVR_76015_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "N", "P", "E", "O", "M", "B" ], "lines": [ "line D C M", "line A C", "line A M", "line C B", "line D A P B", "line A N", "line N P E O M" ], "circles": [ "\\odot O lieson N A C M B" ], "semantics": [ "DB \\perp NM on P" ] }, { "diagram": "PGDP/printed/image/MathVR_55282_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "O", "D", "A", "B", "C" ], "lines": [ "line E D", "line C D", "line E F B", "line C A", "line E A", "line A D O B", "line C F" ], "circles": [ "\\odot O lieson A C B F" ], "semantics": [ "CD \\perp AB on D" ] }, { "diagram": "PGDP/printed/image/MathVR_23170_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "A", "C", "B", "M", "Q", "D" ], "lines": [ "line D B", "line M P", "line P D", "line Q P", "line A P B", "line C M B", "line C Q A", "line Q M D" ], "circles": [], "semantics": [ "MP \\perp QD on M", "AB \\perp CA on A" ] }, { "diagram": "PGDP/printed/image/MathVR_66442_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "F", "B", "D", "A" ], "lines": [ "line A D", "line E F", "line B E C", "line A F", "line B A", "line C F D", "line A E" ], "circles": [], "semantics": [ "BC \\perp AE on E", "AF \\perp CD on F" ] }, { "diagram": "PGDP/printed/image/MathVR_45977_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "A", "C", "O", "P", "B" ], "lines": [ "line A O", "line A D B P C", "line O D", "line O P" ], "circles": [ "\\odot O lieson B A" ], "semantics": [ "AC \\perp OD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_39280_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E" ], "lines": [ "line A C", "line B A", "line B E D C", "line A D", "line A E" ], "circles": [], "semantics": [ "AC \\perp BA on A", "BC \\perp AD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_40979_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "E" ], "lines": [ "line B E", "line C E D", "line A B D", "line A C", "line C B" ], "circles": [], "semantics": [ "BE \\perp CB on B", "AC \\perp CB on C" ] }, { "diagram": "PGDP/printed/image/MathVR_21208_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C", "E" ], "lines": [ "line A E", "line A D", "line B D C", "line A C", "line A B", "line E D" ], "circles": [], "semantics": [ "m \\angle CDE = m \\angle 2", "m \\angle EAC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_20997_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "C", "E", "O", "A" ], "lines": [ "line A C", "line B E O A", "line B D C", "line A D" ], "circles": [ "\\odot O lieson A D E" ], "semantics": [ "AC \\perp BC on C", "m \\angle OAD = m \\angle 1", "m \\angle CAD = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_8375_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "D", "O", "B" ], "lines": [ "line B D", "line A O B", "line C D" ], "circles": [ "\\odot O lieson B D C A" ], "semantics": [ "BD \\perp CD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_51942_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "E", "C", "A" ], "lines": [ "line A C", "line B A", "line D A", "line D E", "line B E C", "line A E" ], "circles": [], "semantics": [ "m \\angle CAE = m \\angle 2", "m \\angle BAD = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_54909_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "A", "D", "B", "P", "C" ], "lines": [ "line P A", "line C B", "line D C", "line P C", "line A F B", "line P F", "line D A", "line P B" ], "circles": [], "semantics": [ "AB \\perp PF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_13545_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "O", "A", "B", "D", "C" ], "lines": [ "line C E B", "line A E D", "line C D", "line C A", "line A O B" ], "circles": [ "\\odot O lieson A C D B" ], "semantics": [ "m \\angle CEA = m \\angle \\alpha" ] }, { "diagram": "PGDP/printed/image/MathVR_69894_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "C", "A", "F", "G", "D", "B", "H" ], "lines": [ "line B D A", "line B G H E", "line C H D", "line C E A", "line B F C", "line F G D", "line G A" ], "circles": [], "semantics": [ "BA \\perp CD on D", "BE \\perp CA on E" ] }, { "diagram": "PGDP/printed/image/MathVR_54067_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "B", "E'", "D", "C" ], "lines": [ "line A E E' B", "line C D B", "line A C", "line E D", "line D E'" ], "circles": [], "semantics": [ "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_15368_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "M", "N" ], "lines": [ "line A D", "line A B C", "line A M N", "line D B", "line C E N", "line E B", "line D M E" ], "circles": [], "semantics": [ "AC \\perp DA on A", "NC \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_11605_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "D", "C", "B", "A", "H", "E" ], "lines": [ "line E H", "line B F", "line B E", "line D F C", "line A E", "line A D", "line A B H", "line B C" ], "circles": [], "semantics": [ "DC \\perp AD on D", "AD \\perp AH on A", "BE \\perp BC on B" ] }, { "diagram": "PGDP/printed/image/MathVR_51057_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D", "G", "P", "E", "F" ], "lines": [ "line A D", "line D E", "line D P B", "line P C", "line D F C", "line C E", "line B C G", "line A P F E G", "line A B" ], "circles": [], "semantics": [ "DC \\perp BG on C" ] }, { "diagram": "PGDP/printed/image/MathVR_78891_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "E", "B", "D", "O" ], "lines": [ "line D C", "line C B", "line A C", "line C O", "line D E A", "line A O B" ], "circles": [ "\\odot O lieson A E C B" ], "semantics": [ "DC \\perp DA on D", "m \\angle CAE = m \\angle 1", "m \\angle ACO = m \\angle 2", "m \\angle CAO = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_15140_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "A", "O", "B" ], "lines": [ "line A C B", "line O D B", "line C D" ], "circles": [ "\\odot O lieson A B" ], "semantics": [ "AB \\perp CD on C" ] }, { "diagram": "PGDP/printed/image/MathVR_45647_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "C", "H", "D" ], "lines": [ "line A D C", "line B H D", "line B C", "line A E B", "line E H C" ], "circles": [], "semantics": [ "AB \\perp EC on E", "AC \\perp BD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_54405_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "B", "O" ], "lines": [ "line C A", "line D A B", "line O A", "line O B" ], "circles": [ "\\odot O lieson B" ], "semantics": [ "DB \\perp OB on B", "m \\angle CAD = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_62866_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "G", "D", "A", "C", "O", "F", "E" ], "lines": [ "line B F C", "line E O G", "line B O", "line A E B", "line D G C", "line O F", "line O C" ], "circles": [ "\\odot O lieson E F G" ], "semantics": [ "m \\angle GOC = m \\angle 4", "m \\angle BOF = m \\angle 2", "m \\angle EOB = m \\angle 1", "m \\angle FOC = m \\angle 3" ] }, { "diagram": "PGDP/printed/image/MathVR_59505_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "F", "B", "C" ], "lines": [ "line C B", "line A E F B", "line C F", "line C A", "line C E" ], "circles": [], "semantics": [ "CB \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_78174_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "O", "P", "D", "B", "F", "E" ], "lines": [ "line A O", "line D O", "line O B", "line E O", "line F O", "line P F B", "line E D F", "line P E A" ], "circles": [ "\\odot O lieson A H D I B" ], "semantics": [ "m \\angle DOF = m \\angle 3", "m \\angle AOE = m \\angle 1", "m \\angle DOE = m \\angle 2", "m \\angle BOF = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/MathVR_64111_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "C" ], "lines": [ "line A C", "line A B", "line A D", "line B D C" ], "circles": [], "semantics": [ "AB = c", "AC = b", "DB = a" ] }, { "diagram": "PGDP/printed/image/MathVR_31710_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "B", "E", "A" ], "lines": [ "line A E", "line E D", "line C D", "line B A", "line B C", "line B E" ], "circles": [], "semantics": [ "m \\angle AEB = m \\angle \\theta" ] }, { "diagram": "PGDP/printed/image/MathVR_16968_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "D", "E", "F", "G" ], "lines": [ "line C F", "line C E D", "line B C", "line B D", "line A D G F", "line C G", "line B E F", "line B A" ], "circles": [], "semantics": [ "AF \\perp BA on A", "AF \\perp CG on G" ] }, { "diagram": "PGDP/printed/image/MathVR_68877_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "A", "C", "P" ], "lines": [ "line A C", "line B P", "line A P D", "line B D C", "line A B", "line P C" ], "circles": [], "semantics": [ "EA = p" ] }, { "diagram": "PGDP/printed/image/MathVR_8155_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "E", "D", "O", "H", "F", "A" ], "lines": [ "line A E O B", "line A H C", "line B C D", "line E H F D", "line C F" ], "circles": [ "\\odot O lieson A C B" ], "semantics": [ "AB \\perp ED on E" ] }, { "diagram": "PGDP/printed/image/MathVR_22462_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "B", "E", "C", "D", "A" ], "lines": [ "line E D", "line A D C", "line A E O B", "line B D", "line B C", "line O D" ], "circles": [ "\\odot O lieson E D B" ], "semantics": [ "ED \\perp BD on D", "AC \\perp BC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_30262_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "E", "F", "C", "A", "B" ], "lines": [ "line a lieson D C", "line b lieson A E B F", "line C F", "line A D", "line E C", "line C B" ], "circles": [], "semantics": [ "line b \\perp CF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_57088_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "F", "C", "E", "G", "D" ], "lines": [ "line E F", "line D C", "line B E D", "line A D", "line B F C", "line E G", "line A B", "line G C", "line D G F" ], "circles": [], "semantics": [ "EF \\perp BD on E" ] }, { "diagram": "PGDP/printed/image/MathVR_38327_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "A", "C", "H", "N", "M", "D" ], "lines": [ "line M E N", "line D N C", "line M H", "line A M D", "line B H N", "line B C", "line E H", "line A B", "line M B" ], "circles": [], "semantics": [ "MH \\perp BN on H" ] }, { "diagram": "PGDP/printed/image/MathVR_16071_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D" ], "lines": [ "line A D", "line B C", "line D C", "line A C", "line A B" ], "circles": [], "semantics": [ "BC = 6", "AD = 6", "AB = 4", "DC = 4" ] }, { "diagram": "PGDP/printed/image/MathVR_54296_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "E", "A" ], "lines": [ "line A E C", "line D E", "line B D C", "line A B", "line A D" ], "circles": [], "semantics": [ "AC \\perp AB on A", "m \\angle BAD = m \\angle 1", "m \\angle EDC = m \\angle 3", "m \\angle BDA = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_73724_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "M", "C", "F", "E", "A", "D", "P" ], "lines": [ "line D E C", "line M D", "line A P B", "line A D", "line M P F E", "line M B C", "line A M", "line F C" ], "circles": [], "semantics": [ "AB \\perp MC on B" ] }, { "diagram": "PGDP/printed/image/MathVR_9196_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "C", "E", "F", "A" ], "lines": [ "line A F C", "line E D", "line B D C", "line A E B", "line E F", "line F D" ], "circles": [], "semantics": [ "AC \\perp AB on A", "ED \\perp FD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_66719_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "D", "B", "F", "C", "G" ], "lines": [ "line C E B", "line E F A", "line C F G D", "line A G", "line A D B", "line C A" ], "circles": [], "semantics": [ "CD \\perp AG on G" ] }, { "diagram": "PGDP/printed/image/MathVR_32163_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "D", "B", "F", "M", "C" ], "lines": [ "line A C F", "line D F", "line B E A", "line M D", "line E D", "line A D", "line B M C", "line C D" ], "circles": [], "semantics": [ "MD \\perp BC on M", "BA \\perp ED on E", "AF \\perp DF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_65030_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "F", "E" ], "lines": [ "line A E C", "line B F A", "line F D", "line B D C", "line F E", "line D E" ], "circles": [], "semantics": [ "FD \\perp DE on D" ] }, { "diagram": "PGDP/printed/image/MathVR_53474_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "O", "P", "C", "A", "D" ], "lines": [ "line A D", "line A O B", "line D P B", "line O P C" ], "circles": [ "\\odot O lieson A D C B" ], "semantics": [ "AB \\perp OC on O" ] }, { "diagram": "PGDP/printed/image/MathVR_15916_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "E", "D" ], "lines": [ "line A D", "line B C", "line D E C", "line A E", "line A B" ], "circles": [], "semantics": [ "DC \\perp AE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_15486_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "B", "A", "E", "C", "O", "P", "D" ], "lines": [ "line P O", "line D C", "line B F O D", "line A D", "line P F", "line B C", "line A E O C", "line P E", "line A P B" ], "circles": [], "semantics": [ "BD \\perp PF on F", "AC \\perp PE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_46294_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "A", "C", "O", "F", "D" ], "lines": [ "line E C", "line D C", "line B O E", "line A E D", "line B C", "line F E", "line A F B", "line F O C" ], "circles": [], "semantics": [ "m \\angle CED = m \\angle 2", "m \\angle AEF = m \\angle 1", "m \\angle ECD = m \\angle 3", "m \\angle OBC = m \\angle 5", "m \\angle OBF = m \\angle 4" ] }, { "diagram": "PGDP/printed/image/MathVR_78555_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C", "E", "D", "P", "F" ], "lines": [ "line P E", "line F P", "line A D F B", "line A P", "line A E C", "line D P" ], "circles": [], "semantics": [ "PE \\perp AC on E" ] }, { "diagram": "PGDP/printed/image/MathVR_44342_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "D", "O", "A", "P" ], "lines": [ "line C O", "line A O P B", "line C P D" ], "circles": [ "\\odot O lieson A D B C" ], "semantics": [ "AB \\perp CD on P" ] }, { "diagram": "PGDP/printed/image/MathVR_78919_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "F", "E", "D", "G", "H" ], "lines": [ "line B C", "line B D E G", "line E C", "line A D H C", "line B H", "line A G F", "line A B", "line E F", "line C F" ], "circles": [], "semantics": [ "EC \\perp EF on E", "BC \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_74923_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "O", "A", "E", "C", "B", "F", "D" ], "lines": [ "line C E", "line D B", "line A E", "line A O B", "line D E F O", "line C F B", "line C A" ], "circles": [ "\\odot O lieson A C E B" ], "semantics": [ "DO \\perp CB on F" ] }, { "diagram": "PGDP/printed/image/MathVR_10643_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B" ], "lines": [ "line C B", "line A C", "line D C", "line A B", "line D A" ], "circles": [], "semantics": [ "m \\angle ACD = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_6913_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "E", "D", "M", "O", "C" ], "lines": [ "line A C M", "line D M", "line B E A", "line E D", "line A D", "line B C" ], "circles": [ "\\odot O lieson A C D B" ], "semantics": [ "BA \\perp ED on E" ] }, { "diagram": "PGDP/printed/image/MathVR_65263_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "M", "B", "F", "A", "C", "E", "G", "H" ], "lines": [ "line E M", "line D F H C", "line A D", "line G M", "line B M C", "line M F", "line A G E B", "line M H" ], "circles": [], "semantics": [ "DC \\perp MH on H", "GM \\perp AB on G" ] }, { "diagram": "PGDP/printed/image/MathVR_61145_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "O_{1}", "E", "O", "A", "B" ], "lines": [ "line D E", "line C E O", "line A D C", "line A O_{1} O B" ], "circles": [ "\\odot O lieson A C B", "\\odot O_{1} lieson A D O" ], "semantics": [ "DE \\perp CO on E" ] }, { "diagram": "PGDP/printed/image/MathVR_52360_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "E", "B", "O", "F" ], "lines": [ "line A F C", "line F O", "line C O", "line C E B", "line O E" ], "circles": [ "\\odot O lieson F E" ], "semantics": [ "m \\angle OCE = m \\angle 1", "m \\angle FCO = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_43623_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "G", "F", "O", "E", "C", "D", "A" ], "lines": [ "line A F D", "line C O F", "line A O E B G", "line C G", "line A C", "line C E D", "line O D" ], "circles": [ "\\odot O lieson A D B C" ], "semantics": [ "AG \\perp CD on E" ] }, { "diagram": "PGDP/printed/image/MathVR_76629_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "A", "C", "P", "F", "E" ], "lines": [ "line A F C", "line E C", "line A P D", "line A E", "line B P", "line B D C", "line A B", "line P C", "line E F D" ], "circles": [], "semantics": [ "AD \\perp EA on A", "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_75966_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "A", "D", "E", "C'" ], "lines": [ "line C E A", "line E C'", "line B A", "line D E", "line C D B", "line D C'", "line C' A" ], "circles": [], "semantics": [ "CA \\perp CB on C" ] }, { "diagram": "PGDP/printed/image/MathVR_16841_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "A", "B", "O" ], "lines": [ "line C B", "line A C", "line A O", "line A B", "line O B" ], "circles": [], "semantics": [ "m \\angle ABO = m \\angle 2", "m \\angle OAB = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_63704_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "B", "O", "D" ], "lines": [ "line D B", "line A O D", "line A B", "line C O B", "line C A" ], "circles": [], "semantics": [ "DB \\perp AD on D", "CB \\perp CA on C" ] }, { "diagram": "PGDP/printed/image/MathVR_73344_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "F", "C", "B", "A", "D" ], "lines": [ "line D E", "line D F", "line C E F A", "line B D A", "line B C" ], "circles": [], "semantics": [ "DF \\perp CA on F" ] }, { "diagram": "PGDP/printed/image/MathVR_41469_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "B", "D", "C", "F", "A" ], "lines": [ "line A C", "line A B", "line F E", "line B E D C", "line A D", "line A E", "line F A", "line F B" ], "circles": [], "semantics": [ "m \\angle BAF = m \\angle 4", "m \\angle CAD = m \\angle 3", "m \\angle DAE = m \\angle 2", "m \\angle ABF = m \\angle 5", "m \\angle BAE = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_38611_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "G", "B", "C", "F", "H", "E", "A", "D" ], "lines": [ "line A E", "line D E C", "line A H G", "line A D", "line B E", "line B G C", "line A F B", "line F H E" ], "circles": [], "semantics": [ "DC \\perp BC on C", "AG \\perp BC on G" ] }, { "diagram": "PGDP/printed/image/MathVR_41105_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "C", "G", "B", "F", "E", "H" ], "lines": [ "line A B", "line A E C", "line E D", "line C D G B", "line A H G", "line A F D", "line E F H B" ], "circles": [], "semantics": [ "m \\angle ABF = m \\angle 6", "m \\angle DEF = m \\angle 5", "m \\angle GAF = m \\angle 3", "m \\angle EAF = m \\angle 4", "m \\angle GBF = m \\angle 7", "m \\angle BAG = m \\angle 2", "m \\angle GDF = m \\angle 8", "m \\angle AHF = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_64080_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "A", "G", "B", "F", "H", "N", "M", "D" ], "lines": [ "line C H", "line M E", "line D G", "line D C", "line A E G H F B", "line N F", "line M N", "line D M A", "line C N B" ], "circles": [], "semantics": [ "CH \\perp AB on H", "AB \\perp NF on F", "DG \\perp AB on G", "ME \\perp AB on E" ] }, { "diagram": "PGDP/printed/image/MathVR_21961_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "D", "F", "C", "E", "A" ], "lines": [ "line A E F", "line D A", "line B F C", "line D E C", "line A B" ], "circles": [], "semantics": [ "DA \\perp AB on A", "BC \\perp AB on B" ] }, { "diagram": "PGDP/printed/image/MathVR_75020_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "Q", "H", "O", "A", "N", "E", "F", "M", "C" ], "lines": [ "line E H", "line O D", "line M N", "line F O", "line B E C F M", "line E O", "line B A", "line A H Q O N", "line C Q D" ], "circles": [ "\\odot O lieson A E N D" ], "semantics": [ "FO \\perp BM on F", "BM \\perp CD on C" ] }, { "diagram": "PGDP/printed/image/MathVR_71503_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "C", "B", "G", "H", "A", "E" ], "lines": [ "line B H E A", "line C E", "line E D", "line C D G A", "line E G", "line B C", "line H C" ], "circles": [], "semantics": [ "BA \\perp HC on H", "m \\angle EAG = 30", "m \\angle HBC = m \\angle DGE = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_16151_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A", "D" ], "lines": [ "line C D", "line C A", "line B A", "line B D", "line B C" ], "circles": [], "semantics": [ "CD \\perp BD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_21895_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "E", "F", "O", "C", "D", "G" ], "lines": [ "line E B O C", "line A F G C", "line E D F", "line A D B", "line D O" ], "circles": [ "\\odot O lieson B D G C" ], "semantics": [ "AC \\perp EF on F" ] }, { "diagram": "PGDP/printed/image/MathVR_55687_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "Q", "A", "C", "S", "R", "P" ], "lines": [ "line R P", "line B P C", "line B R A", "line A Q S C", "line P S", "line P Q" ], "circles": [], "semantics": [ "AC \\perp PS on S", "RP \\perp BA on R" ] }, { "diagram": "PGDP/printed/image/MathVR_21102_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "D" ], "lines": [ "line A C", "line B D C", "line A D", "line B A" ], "circles": [], "semantics": [ "m \\angle CAB = 120" ] }, { "diagram": "PGDP/printed/image/MathVR_31258_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "A", "C", "E", "D" ], "lines": [ "line E C", "line D C", "line A D", "line B C", "line D E", "line A E B" ], "circles": [], "semantics": [ "AD \\perp AB on A", "m \\angle CDE = m \\angle 1", "m \\angle ECD = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_50960_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "E" ], "lines": [ "line D C", "line A E B", "line C B", "line A C", "line D E", "line D A" ], "circles": [], "semantics": [ "CB \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_48016_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "B", "C", "D", "A" ], "lines": [ "line A D C", "line P D", "line B P C", "line A B", "line A P" ], "circles": [], "semantics": [ "m \\angle DPA = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_44658_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "F", "D", "C", "E", "O", "A" ], "lines": [ "line A D E", "line F B O A", "line F C E", "line A C" ], "circles": [ "\\odot O lieson A D C B" ], "semantics": [ "AE \\perp FE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_38520_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "C", "B", "D", "G" ], "lines": [ "line C D", "line C G", "line A D G B", "line E C B", "line C A" ], "circles": [], "semantics": [ "CD \\perp EB on C" ] }, { "diagram": "PGDP/printed/image/MathVR_74464_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "E", "C", "F", "D", "A" ], "lines": [ "line A C", "line A D", "line E D", "line B D", "line B C", "line B F E A", "line F D" ], "circles": [], "semantics": [ "m \\angle EDF = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_956_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "E", "A", "D", "B", "F", "C" ], "lines": [ "line C B", "line D C", "line A E F B", "line C F", "line D E", "line D A" ], "circles": [], "semantics": [ "m \\angle CBF = m \\angle \\alpha", "m \\angle EAD = m \\angle \\beta" ] }, { "diagram": "PGDP/printed/image/MathVR_70807_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "F", "E", "O", "D", "G", "A" ], "lines": [ "line B E A", "line E G F", "line E D", "line B O", "line C E", "line B C", "line C O G D A", "line D F", "line E O" ], "circles": [ "\\odot O lieson C E D F" ], "semantics": [ "m \\angle BOE = m \\angle 3", "m \\angle EDG = m \\angle 2", "m \\angle ECO = m \\angle 4", "m \\angle BOC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_65739_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "B", "A'''", "F", "D", "A" ], "lines": [ "line A D C", "line B C A'''", "line A F B", "line F D", "line D A'''" ], "circles": [], "semantics": [ "m \\angle CBF = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_51051_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "E", "F", "A", "D", "B", "O" ], "lines": [ "line E C A", "line F B O A", "line F D E" ], "circles": [ "\\odot O lieson D B A C" ], "semantics": [ "EA \\perp FE on E" ] }, { "diagram": "PGDP/printed/image/MathVR_79128_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "F", "E", "D", "A", "N", "H", "M", "P", "B", "C" ], "lines": [ "line A N M C", "line F N H D", "line F M P E", "line D E", "line A B", "line B H P C" ], "circles": [], "semantics": [ "FD \\perp DE on D", "AC \\perp AB on A" ] }, { "diagram": "PGDP/printed/image/MathVR_65850_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "B", "A", "D", "M", "F", "C", "E" ], "lines": [ "line A D", "line D M", "line B N C M", "line B D", "line E F", "line D N", "line D F C", "line A C", "line A E B" ], "circles": [], "semantics": [ "BM \\perp DN on N" ] }, { "diagram": "PGDP/printed/image/MathVR_65319_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "N", "A", "D", "P", "B", "M", "C" ], "lines": [ "line C B", "line M A", "line M N", "line D M C", "line A N P B", "line M P", "line D A" ], "circles": [], "semantics": [ "MN \\perp AB on N" ] }, { "diagram": "PGDP/printed/image/MathVR_42140_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "C", "D", "B" ], "lines": [ "line D C", "line C B", "line A B", "line D B", "line D A" ], "circles": [], "semantics": [ "DB \\perp DA on D", "m \\angle BAD = 60" ] }, { "diagram": "PGDP/printed/image/MathVR_30307_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "B", "C", "E", "D", "A", "O" ], "lines": [ "line E O C", "line A D C", "line B O D", "line B C", "line A E B", "line E D" ], "circles": [], "semantics": [ "m \\angle OED = m \\angle 5", "m \\angle ADE = m \\angle 2", "m \\angle AED = m \\angle 1", "m \\angle OCB = m \\angle 4", "m \\angle OBC = m \\angle 3", "m \\angle ODE = m \\angle 6" ] }, { "diagram": "PGDP/printed/image/MathVR_75188_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "M", "A", "F", "C", "D", "E", "B" ], "lines": [ "line E F D", "line M F B C", "line E M", "line E B", "line A B", "line A C", "line B D" ], "circles": [], "semantics": [ "MC \\perp EM on M" ] }, { "diagram": "PGDP/printed/image/MathVR_12698_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "E", "B", "C", "O", "D" ], "lines": [ "line B O", "line B D C", "line A C", "line A B", "line O D", "line B E", "line O C", "line E C" ], "circles": [ "\\odot O lieson A C E B" ], "semantics": [ "BC \\perp OD on D" ] }, { "diagram": "PGDP/printed/image/MathVR_25677_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "D", "F", "E", "C" ], "lines": [ "line B C F", "line B D A", "line D C", "line A E C", "line D E F" ], "circles": [], "semantics": [ "BA \\perp DC on D", "BF \\perp AC on C" ] }, { "diagram": "PGDP/printed/image/MathVR_12236_img3.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "P", "B", "E", "C", "A", "F", "H", "M", "D", "O" ], "lines": [ "line B O H A", "line D A", "line P D F H E", "line D M O", "line C P", "line C M F A" ], "circles": [ "\\odot O lieson B C D A E" ], "semantics": [ "BA \\perp PE on H" ] }, { "diagram": "PGDP/printed/image/MathVR_17758_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "D", "B", "C", "E" ], "lines": [ "line A C", "line A E B", "line E D", "line B D C", "line A D" ], "circles": [], "semantics": [ "m \\angle EDA = m \\angle 3", "m \\angle EAD = m \\angle 1", "m \\angle DAC = m \\angle 2" ] }, { "diagram": "PGDP/printed/image/MathVR_24449_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "D", "B", "E", "O", "A", "P", "C", "F" ], "lines": [ "line P F B", "line C B", "line O C", "line C F E D", "line P D", "line O D", "line A O E B" ], "circles": [ "\\odot O lieson A P C B D" ], "semantics": [ "m \\angle FBC = m \\angle 1" ] }, { "diagram": "PGDP/printed/image/MathVR_39994_img2.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "C", "D", "F", "E", "O", "A", "B" ], "lines": [ "line C B", "line A F C", "line F O", "line C E D", "line C O", "line A O E B" ], "circles": [ "\\odot O lieson A C B D" ], "semantics": [ "CD \\perp AB on E", "AC \\perp FO on F" ] }, { "diagram": "PGDP/printed/image/MathVR_23404_img1.png", "style": "printed", "split": "test", "category": "plane geometry", "points": [ "A", "B", "C" ], "lines": [ "line A C", "line A B", "line C B" ], "circles": [], "semantics": [ "m \\angle ABC = 45", "m \\angle CAB = 30" ] }, { "diagram": "SGDP/image/2416_auxiliary.png", "split": "test", "category": "solid geometry", "structure": [ "Pyramid P-ABC" ], "points": [ "P", "A", "B", "C", "O", "G", "E", "F" ], "lines": [ "line A B", "line B E C", "line C G A", "line P A", "line P B", "line P F C", "line A O E", "line A F", "line E F", "line E G", "line F G", "line O F", "line O G" ], "planes": [ "plane A B E C G O", "plane P A B", "plane P B E C F", "plane P F C G A", "plane A F E O", "plane F G E", "plane F O G" ], "circles": [], "semantics": [] }, { "diagram": "SGDP/image/33159_img1.png", "split": "test", "category": "solid geometry", "structure": [ "Cube ABCD-A_{1}B_{1}C_{1}D_{1}" ], "points": [ "A", "B", "C", "D", "A_{1}", "B_{1}", "C_{1}", "D_{1}", "E" ], "lines": [ "line A B", "line B C", "line C D", "line D A", "line A_{1} B_{1}", "line B_{1} C_{1}", "line C_{1} E D_{1}", "line D_{1} A_{1}", "line A A_{1}", "line B B_{1}", "line C C_{1}", "line D D_{1}", "line D E", "line A E", "line B E", "line C E" ], "planes": [ "plane A B C D", "plane A_{1} B_{1} 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