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Let \(X, Y, \) and \(Z\) be points on a circle. Let line \(XY\) and the tangent to the circle at \(Z\) intersect at \(W.\) If \(WX=4, WZ=8\), and \(\overline{WY} \perp \overline{WZ}\), then find \(YZ.\)

 

I know there is another thread on this, but it doesn't seem like it is right.

 Jun 16, 2021
 #1
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We can use power of a point to find XY. 

8^2 = 4 * xy

xy = 16

 

Now we have a right triangle with legs 20 and 8. 

sqrt(20^2 + 8^2) = sqrt(464) = 4sqrt(29)

 

=^._.^=

 Jun 17, 2021

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