Question 156
Let $P$ be point inside of the triangle $ABC$. Let $S$ be the perpendicular foot from $P$ to $AB$ and $T$ be the perpendicular foot from $P$ to $BC$. Let line $AC$ intersected to the circumcircle of $STA$ and circumcircle of $STC$ at point $X$ and $Y$, respectively. If $R$ is the intersection of the lines $SY$ and $TX$ then prove that $PR \perp AC$.