Question 81
Let $ABC$ be an arbitrary triangle with $AB \gt AC$. The point $P \in (AB)$ has the property that $\angle ACP \equiv \angle ABC$. Let $D$ be the reflection of $P$ across $AC$ and let $E$ be the point where the circumcircle of triangle $BCD$ meets the line $AC$ a second time. Prove that $AE = AC$.