Chords $\overline{WY}$ and $\overline{XZ}$ of a circle are perpendicular. If $XV = 4$, $WV = 3$, and $VZ = 9$, then find $YZ$.
By the theory of intersecting chords.....
XV * ZV = WV * YV ....so....
4 * 9 = 3 * YV divide both sides by 3
[ 4 * 9 ] / 3 = YV
36 / 3 = YV = 12
And since the chords are perpendicular, by the Pythagorean Theorem.......
ZV^2 + YV^2 = YZ^2
9^2 + 12^2 = YZ^2
225 = YZ^2 take the square root of both sides
15 = YZ