Question 65
Let $ABC$ be an acute triangle ($AB \lt BC \lt AC$) with circumcircle $\Gamma$. Assume there exists $X \in AC$ satisfying $AB = BX$ and $AX = BC$. Points $D, E \in \Gamma$ are taken such that $\angle ADB \lt 90^\circ$, $DA = DB$ and $BC = CE$. Let $P$ be the intersection point of $AE$ with the tangent line to $\Gamma$ at $B$, and let $Q$ be the intersection point of $AB$ with tangent line to $\Gamma$ at $C$. Show that the projection of $D$ onto $PQ$ lies on the circumcircle of $\triangle PAB$.