Question 65
In triangle $ABC$, $\alpha=\angle BAC$ is strictly the smallest angle. Let $P$ lie on side $BC$. Choose $D$ on line $AB$ with $B$ between $A,D$ and $\angle BPD=\alpha$, and $E$ on line $AC$ with $C$ between $A,E$ and $\angle EPC=\alpha$. Prove that $AP,BE,CD$ are concurrent if and only if $AP\perp BC$.