Question

$\overleftrightarrow{wx}$ is tangent to $\odot v$. what is $wx$?
(there is a diagram with a circle centered at $v$, a tangent segment $wx$ where $w$ is on the circle, $vw = 8$ in, and $vx = 17$ in. the question asks for the length of $wx$.)

Explanation:

Step1: Use the property of tangent to a circle

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle VWX = 90^{\circ}$, and $\triangle VWX$ is a right - triangle.

Step2: Apply the Pythagorean theorem

In right - triangle $\triangle VWX$, by the Pythagorean theorem $VX^{2}=VW^{2}+WX^{2}$. We know that $VX = 17$ in and $VW = 8$ in. Then $WX^{2}=VX^{2}-VW^{2}$.
Substitute the values: $WX^{2}=17^{2}-8^{2}=289 - 64=225$.
Take the square root of both sides: $WX=\sqrt{225}=15$.

Answer:

$15$