## Problem of the Day #124: Circle Inscribed Within an Isosceles TrapezoidJuly 21, 2011

Posted by Saketh in : potd , trackback

A circle is inscribed inside isosceles trapezoid $ABCD$. The circle intersects diagonal $\overline{AC}$ twice, once at point $E$ and again at point $F$. Suppose $E$ lies between $A$ and $F$. The value of

$$\frac{AF \cdot EC}{AE \cdot FC}$$

can be expressed in the form $a + \sqrt{b}$, where $a$ and $b$ are positive integers. Compute the value of $ab$.