Problem - 3122
Chords $AB$ and $CD$ of a given circle are perpendicular to each other and intersect at a right angle at point $E$. If $BE=16$, $DE=4$, and $AD=5$, find $CE$.
First, $ADE$ is a right triangle with hypotenuse 5 and leg 4. Thus, by the Pythagorean Theorem, $AE = 3$.
Then, applying the Power of a Point Theorem gives $AE\cdot BE = CE\cdot DE$, or $3\cdot 16 = x\cdot 4$. Solving gives $x = \boxed{12}$.