RS-SMO 2019 Problem 3

Let $k$ be the circle inscribed in convex quadrilateral $ABCD$ . Lines $AD$ and $BC$ meet at $P$ ,and circumcircles of $\triangle PAB$ and $\triangle PCD$ meet in $X$ . Prove that tangents from $X$ to $k$ form equal angles with lines $AX$ and $CX$ .