Question 133
Let $\Gamma$ be a circle and $P$ a point outside $\Gamma$. A tangent from $P$ to the circle touches it at $A$. Another straight line through $P$ intersects $\Gamma$ at the various points $B$ and $C$. The bisector of $\measuredangle A P B$ cuts $A B$ into $D$ and $A C$ into $E$. Prove that triangle $A D E$ is isosceles.