Question 77
Let $ABC$ be a triangle and $D$ a point in the interior of segment $BC$. Let $X$ be another point in the interior of segment $BC$, different from $D$, and let $Y$ be the intersection point of $AX$ with the circumcircle of $ABC$ (other than $A$). Let $P$ be the second intersection point of the circumcircles of $ABC$ and $DXY$. Prove that $P$ is independent of the choice of $X$.