| [0.27s -> 14.86s] Hello, this is Mr. Kinyanola, and I'm going to help you find segment lengths when you have a tangent line. So, if you didn't see the video on tangent lines and radii, it's just a previous video. |
| [14.86s -> 28.37s] video i suggest you watch it because it's so fascinating um so uh but if you didn't think it's fascinating then whatever i'm not hurt okay so yeah not hurt so but just watch it again |
| [28.37s -> 42.80s] And again and again. So find the segment length indicated. So this line right here. Assume that lines which appear to be tangent are tangent. So this line right here, it's telling us that this line is tangent. |
| [42.80s -> 55.31s] So if you guys remember, when a line is tangent to a circle and a radius intersects that tangent line at the point of tangency where the line... |
| [55.31s -> 66.62s] touches the circle then the radius and the tangent line are perpendicular. Remember perpendicular means that they make right angles so this is a right angle. |
| [66.62s -> 80.61s] so what do we have here it looks like we have a right triangle it says find this length right here this is the question mark when we have a right triangle and we have at least information about two sides |
| [80.61s -> 82.93s] we can use the Pythagorean theorem. |
| [83.15s -> 95.92s] So let's use a Pythagorean theorem. Remember the Pythagorean theorem is C squared is equal to A squared plus B squared. And the C is the hypotenuse. The hypotenuse is the side. |
| [95.92s -> 107.62s] that is opposite the right angle here's the right angle and it's looking at the hypotenuse right there so this entire side right here is the hypotenuse |
| [107.62s -> 115.47s] we're trying to just find this but what's the length of this right here do we have any information about this whole thing right here um yeah so |
| [115.73s -> 129.62s] The length from here to here is 4 because that's the radius. So the length of this, our information about C, is 4 plus question mark. |
| [129.65s -> 140.62s] The hypotenuse that we have is 4 plus question mark squared. So this is our C right here. |
| [140.62s -> 150.99s] and we'll set it equal to a squared which is 4 squared plus 4.2 squared so here's our a |
| [150.99s -> 164.45s] Here's our B or this could have been your A. This could have been your B. Doesn't matter. And then let's just grab our calculator and start scoring some numbers. So four squared. Well, we don't need a calculator for that. Hopefully not. Four squared is not eight. |
| [164.45s -> 173.52s] It's 16. But what's this decimal square? So 4.2 squared is 17.65. |
| [173.52s -> 187.79s] four is equal to so now here you're going to be tempted to do some algebra definitely don't be tempted to distribute the square here and here because that's against algebra rules you'll be tempted to |
| [187.79s -> 198.51s] You might write four plus question mark times four plus question mark because that's real algebra, but don't do that. So just bring this down. |
| [199.09s -> 210.86s] okay and let's combine these two like terms so 16 uh so we still have the 17.64 plus 16 which is 33 |
| [211.31s -> 218.69s] Point six four and we'll bring this down four plus question mark squared |
| [218.69s -> 232.75s] and we want to get this question mark by itself so i want to get rid first i want to get rid of the square right here what's the opposite of scoring something yeah i heard you you said square root yeah good so we're going to square root both sides |
| [232.75s -> 241.58s] So the square root of 33.64 is 5.8. |
| [243.12s -> 257.30s] And so now the square and the square roots or the radical cancel each other out. So we just have four plus question mark. And how do we get that question mark by itself? We subtract four from both sides. So the question mark. |
| [257.30s -> 267.25s] 5.8 minus 4 is 1.8. There aren't any units, so we're just going to write units. |
| [267.34s -> 277.60s] That looks like a V, so I'm going to write the word out. So units. So there's your final answer. Question mark is 1.8 units. |
| [277.60s -> 285.10s] and that's how you find a segment length when you have a tangent line and the radius just remember |
| [285.10s -> 296.24s] that the tangent line and the radius are always perpendicular. And if they make a triangle, they make a right triangle. So just use a Pythagorean theorem. |
| [296.24s -> 300.23s] And that's it. I hope that helps. Have a great day. |
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