Problem #PRU-5284

Problem

Let $C_1$ and $C_2$ be two concentric circles with $C_1$ inside $C_2$ and the center $A$. Let $B$ and $D$ be two points on $C_1$ that are not diametrically opposite. Extend the segment $BD$ past $D$ until it meets the circle $C_2$ in $C$. The tangent to $C_2$ at $C$ and the tangent to $C_1$ at $B$ meet in a point $E$. Draw from $E$ the second tangent to $C_2$ which meets $C_2$ at the point $F$. Show that $BE$ bisects angle $\mathrm{\angle }FBC$.