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The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XY = 14$ and $WX = 6,$ find $YZ.$
 Apr 7, 2023
 #1
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The tangent to the circumcircle of a triangle at a point divides the opposite side into segments in the ratio 2:1, with the longer segment being the side that is closer to the tangent point.

In this case, the tangent point is X and the opposite side is XY. Since WX = 6 and XY = 14, the ratio of the segments is 2:1. This means that the length of the segment from X to Z is 2/3 * XY = 34/3

Therefore, YZ = XY - 34/3 = 8/3

 Apr 7, 2023
 #2
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wrong
Guest Apr 7, 2023

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