Question 67
Let $\triangle ABC$ be an acute triangle with circumcircle $\Gamma$, and let $P$ be the midpoint of the minor arc $BC$ of $\Gamma$. Let $AP$ meet $BC$ at $D$, and let $M$ be the midpoint of $AB$. Also, let $E$ be the point such that $AE \perp AB$ and $BE \perp MP$. Prove that $AE = DE$.