The tangent to the circumcircle of triangle WXY at X is drawn, and the line through W that is parallel to this tangent intersects XY at Z If XY=14 and WX=6 find YZ.


 Jun 16, 2022

Let P be the point on the tangent at the bottom of the image.


Note that \(\angle PXZ = \angle XZW\) since they are alternate angles of the pair of parallel lines.

Also, \(\angle PXZ = \angle XWY\) since they are angles in alternate segments.


Therefore \(\angle XZW = \angle XWY\). Also, \(\angle ZXW = \angle WXY\) since they are the same angle.

By AA postulate, \(\triangle XZW \sim \triangle XWY\).


Let YZ = t. Then by similar triangles, \(\dfrac{XZ}{XW} = \dfrac{XW}{XY}\). i.e., \(\dfrac{14 - t}{6} = \dfrac{6}{14}\).


Can you take it from here?

 Jun 16, 2022

Thanks for the help!

Guest Jun 16, 2022

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