IMO 2025 — Complete Shortlist Question 17

Let $ABC$ be a triangle such that $\angle A$ is obtuse. Let $D$ and $E$ be points on sides $AB$ and $AC$, respectively, such that $BDEC$ is cyclic. Suppose the circumcircle of triangle $ADE$ intersects side $BC$ at two points $X$ and $Y$, where $B, X, Y$ and $C$ lie in that order. Let the circumcircles of triangles $BDX$ and $CEY$ be $\Omega$ and $\Gamma$, respectively. Let $P$ be a point such that $PD$ is tangent to $\Omega$ and $PE$ is tangent to $\Gamma$. Let $Q$ be a point such that $QB$ is tangent to $\Omega$ and $QC$ is tangent to $\Gamma$.

Prove that points A, P and Q are collinear.