difficulty stringclasses 2
values | image imagewidth (px) 124 959 | question stringlengths 128 357 | answer stringclasses 4
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|---|---|---|---|
easy | Between (i) and (ii), which best describes the image? (i) All edges OR, RK, and KO share the same length in triangle ORK. (ii) Triangle OKR has altitudes converging at J, defining it as the orthocenter. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) Point N results from flipping Z across E. (ii) There exist a triangle EDZ with midpoints N, C, Q, and a point S that is the circumcenter of triangle NCQ. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:There exist a square with vertices B, K, D, S. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) Point P is the excenter of triangle LXF that lies opposite to vertex L. (ii) Tangent circles X and F share a contact at U on line HU. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) There exist a configuration where UI is U unit for every K units of IC. (ii) Triangle IUC has two sides in the ratio 1:3. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:A four-sided polygon with corners W, Z, V, L is identified. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:Angle equality TES = SHT is represented by A. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:A four-sided figure is delineated by G, , S, . Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) The right-angle intersection from K to EZ is located at H. (ii) There exist a triangle KHZ that is right-angled and isosceles, with KH = KZ. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:An equivalence as Z occurs between angles ISD and DCI. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:The boundary is a half-circle arc from center Z at distance 1364. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:The angle formed by J, R, X is assigned the value 133°. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:This sector is part of a circle, cut by angle S from center R. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) A single straight path contains points L, A, and S. (ii) Foot G is the meeting point of the perpendicular from S onto line LA. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:Two angles, PUA and RSE, hold an equivalent angle size. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) A 180-degree circular boundary is drawn with N as the midpoint of the diameter. (ii) There exist an inscribed circle in triangle NV, having P as its center. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:DV is cut into three identical portions at S and O. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:A pairing of points M, P and N, B yield the same segment length. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:A right angle occurs where LX intersects LI. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:The midpoint of SW is Q, confirming the symmetry. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:There exist a circle centered at N and a segment of that circle spanning angle H. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:There exist a quadrilateral WVSE having one set of parallel sides. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:I see a right trapezoid KOFO, with KO orthogonal to both KO and OF. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) The perpendicular midpoint line of LA holds Z in its path. (ii) A single straight path contains points D, F, and L. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) There exist an overlap region of circles T, R, defined by intersection N, F. (ii) A four-sided figure NRHT includes a pair of parallel edges. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:Line BS meets line BD at B. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) There exist a circular sector defined by center R, radius 1710, and an angle measure 76°. (ii) A circular shape is drawn with center W and fixed radius K. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:Points U, N, Z, F form a rectangle in the plane. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:Trapezoid FYWN is a polygon with four vertices, two of which form parallel lines. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) I see a right trapezoid YPFM, with YP orthogonal to both YM and PF. (ii) There is an ellipse with focus Y and F in the image. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) There exist a right triangle ARG specifically angled at A. (ii) A circle around G has every boundary point at distance A from G. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:Points H, G, F, W exist where the segment from H to W equals the segment from G to F. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) Point Y is positioned along the ellipse boundary. (ii) Points Y, G, C, and E exist where E is the excenter across from vertex Y in triangle YGC. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) A rectangle YPXE is present. (ii) Circles Y and W meet tangentially at N, while lines XP and PU also contact circle W at E and I, and point X belongs to circle Y. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) In triangle NIB, N is the corner of the right angle. (ii) Points B, N, I, F enclose a rectangle with orthogonal corners. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) There exist lines indicating RE, UI, w are equal and RI, EU, k are equal. (ii) E is the reflection of I when mirrored across U. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) Lines S and H intersect at point J. (ii) There is a right trapezoid SBHJ where SB is perpendicular to SJ and BH. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) The line orthogonal to line GO is TH. (ii) There is an ellipse with focus G and T in the image. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) f indicates that angle QBZ and angle ZTQ share the same measure. (ii) Point Z is obtained by rotating Q around O by 90 degrees. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:There is Triangle YRF. Put your final answer within \boxed{}. | True | |
easy | Between (i) and (ii), which best describes the image? (i) There exist a line CT, circle N, and circle I, with point C on circle N and point T on circle I. (ii) Line s shares the same endpoint I with line IN. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) The midpoint of BZ is I, confirming the symmetry. (ii) A right-angled triangle is formed by Z, B, I, with the right angle located at Z. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:There exist a perpendicular from H to QE that intersects at Z as the foot. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) The ellipse is intersected by the line, generating points P, W in common. (ii) The line does not terminate, yet touches circle P exactly at W. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:A quadrilateral VCXJ is present. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:A pairing of points E, B and Z, H yield the same segment length. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:The entire line VU remains contained in the interior of circle D. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:The perpendicularity of XS and XF highlights their orthogonal relationship. Put your final answer within \boxed{}. | True | |
easy | Between (i) and (ii), which best describes the image? (i) Circle E and line WZ share point C as their unique contact. (ii) There exist points W, E, C such that C is the symmetric counterpart of W about E. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) Convex quadrilateral BICQ is a four-sided figure with all interior angles less than 180 degrees. (ii) Edges QI and BC in this quadrilateral are congruent. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) A point I is situated on circle L, and circle S tangentially contacts circle L and line IF. (ii) There exist a triangle BIF and a point L that is its orthocenter. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) A line crossing the ellipse yields intersection coordinates D, O. (ii) R, H, and M serve as midpoints on each side of triangle CDO, while Q acts as the circumcenter for triangle RHM. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) Circle F encloses Q on its perimeter. (ii) There exist points C, Q, Z, forming angle QCZ with measure F. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) A is obtained by mirroring O over line LU. (ii) A right isosceles triangle AOL exists where sides AL and AO are equal. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) The incircle of triangle PMV is marked by center Z and tangent points E, J, J. (ii) Line e shares the same endpoint M with line ME. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:A single point H is the tangential contact between circles N and R. Put your final answer within \boxed{}. | True | |
easy | Between (i) and (ii), which best describes the image? (i) There exist a geometric scenario with an ellipse and line meeting at J, A. (ii) A, Z, and J all lie on a single straight line. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:Point T is exactly on the ellipse. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:Tangency at T occurs with circle D encircling circle L internally. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) Reflection about line AX places S and H in symmetric positions. (ii) A shared tangent line intersects circle X once at A and circle Z once at M. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) Points B, G, K all lie on a single straight line. (ii) There is an ellipse with focus G and K in the image. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) The ellipse is intersected by the line, generating points A, I in common. (ii) There exist lines A and I that intersect at point O. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:There exist a triangle FGZ and a circle of center J and radius E lying inside it. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:Angle RWG is congruent to angle VZV. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) The measure of U-K is the same as that of R-G. (ii) Line KR is bisecting angle TKU. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) Convex quadrilateral ERXQ is a four-sided figure with all interior angles less than 180 degrees. (ii) Segment XQ forms a right angle with segment XC. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:Circle V has chord TB formed by line MH. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) A three-sided figure U with a specific ratio of edges U and U. (ii) Center U is the midpoint of the straight diameter for this semicircle. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) There exist a configuration where line JT does not exit the interior of circle E. (ii) The angle formed by Y, E, C is assigned the value r. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) Lines N, D, and point F exist with F as their point of intersection. (ii) A set of three points D, N, F defines a triangle. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) Point K is exactly on the ellipse. (ii) Point K is equidistant from the vertices Z, L, and Y in the circumscribed circle. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) There exist a reflective setup with line YU as the mirror line, flipping D to T. (ii) Triangle UTD is set so that angle TUD is 90 degrees. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) The line JX contains O as one of its points. (ii) Triangle OXJ has OX : XJ in a 1:1 proportion. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:There is Triangle JZF. Put your final answer within \boxed{}. | True | |
easy | Between (i) and (ii), which best describes the image? (i) In triangle VWE, V is the corner of the right angle. (ii) Edges VE and WT in this quadrilateral are congruent. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) Points K, Y, J exist such that they are on a common line. (ii) Triangle XKY is set so that angle KXY is 90 degrees. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) There exist a circle around triangle EOJ whose center is B. (ii) The radius J extends from center B to any point on the circle. Put your final answer within \boxed{}. | (i) | |
easy | Answer the following question based on the given image. True or False:Vertices J, E, Z, and L make up a convex four-sided polygon. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:A line crossing the ellipse yields intersection coordinates J, W. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:Point O is positioned along the ellipse boundary. Put your final answer within \boxed{}. | True | |
easy | Between (i) and (ii), which best describes the image? (i) A circle is fully described by center U and distance T as its radius. (ii) Point N is the single intersection of circles T and E, proving tangency. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:The line that contains N also contains I and D. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:Segments EO and EL meet in a perpendicular fashion. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) The measure of angle ZOF is the same as that of angle FHZ, denoted T. (ii) Line g shares the same endpoint F with line FT. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:A line passes through Z, X, and Q without deviation. Put your final answer within \boxed{}. | True | |
easy | Answer the following question based on the given image. True or False:Foot K is the meeting point of the perpendicular from N onto line GJ. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:Center O defines a circle and includes S as a boundary point. Put your final answer within \boxed{}. | False | |
easy | Answer the following question based on the given image. True or False:There is an ellipse with focus X and Z in the image. Put your final answer within \boxed{}. | True | |
easy | Between (i) and (ii), which best describes the image? (i) Triangle JPZ has an excenter opposite J, designated as point A. (ii) This quadrilateral JAZP is identified as a parallelogram. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:Point G is the circumcenter for the circumscriber circle of Triangle LRC. Put your final answer within \boxed{}. | False | |
easy | Between (i) and (ii), which best describes the image? (i) Center T is equidistant from each side of triangle CMZ, forming the incircle. (ii) Two equal angles arise from angle CMJ due to line MX. Put your final answer within \boxed{}. | (ii) | |
easy | Answer the following question based on the given image. True or False:Point P acts as the center of the circumscribed circle around triangle WXJ. Put your final answer within \boxed{}. | True | |
easy | Between (i) and (ii), which best describes the image? (i) A segment NR does not approach or intersect circle X. (ii) A 90-degree rotation around point N transforms X into K. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) Point I lies where Z would be after a quarter-turn about Y. (ii) There exist a triangle IYZ and a circle having center N that is tangent at X, X, and Q. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) There is a 90-degree angle between VP and VE. (ii) There is an ellipse with focus P and V in the image. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) Points X, B, J, and L exist such that L is the centroid of triangle XBJ. (ii) X belongs to circle J. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) The length of PU matches that of CG. (ii) The perpendicular line to CG is formed by points U and P. Put your final answer within \boxed{}. | (i) | |
easy | Between (i) and (ii), which best describes the image? (i) V is the reflection of Q when mirrored across A. (ii) There exist an ellipse and a line that share exactly two intersection points A, Q. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) A configuration exists with circle S, circle N, line DP, and point D on circle S, where circle N is tangent to circle S and line DP. (ii) Three points W, D, S that lie together on a line. Put your final answer within \boxed{}. | (ii) | |
easy | Between (i) and (ii), which best describes the image? (i) Lines BA and RT intersect at point I, forming an angle of S degrees. (ii) A three-sided figure ABR is present where every side length is the same. Put your final answer within \boxed{}. | (ii) |
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