Let X, Y, and Z be points on a circle. Let XY and the tangent to the circle at Z intersect at W. If WX = 4, WZ = 8, and WY is perpendicular to WZ, then find YZ.

*PS - The answer is not 4 * sqrt(29)*

Guest Oct 16, 2020

#3**0 **

Important: **If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant:**

Knowing this, we have:

**WZ ^{2} = WX * WY 8^{2} = 4 ( 4 + XY ) XY = 12**

**YZ = sqrt ( WZ ^{2} + WY^{2} ) = √320 **

Guest Oct 16, 2020