Question 43
Let $ABC$ be a triangle and let the tangent at $B$ to its circumcircle meet the internal bisector of angle $A$ at $P$. The line through $P$ parallel to $AC$ meets $AB$ at $Q$. Assume that $Q$ lies in the interior of segment $AB$ and let the line through $Q$ parallel to $BC$ meet $AC$ at $X$ and $PC$ at $Y$. Prove that $PX$ is tangent to the circumcircle of triangle $XYC$.