Question 96
A convex quadrilateral $A B C D$ is circumscribed about a circle $k$. The lines $A D$ and $B C$ meet at the point $P$, and the circles circumscribed about $\triangle P A B$ and $\triangle P C D$ meet at the point $X$. Prove that the tangents from the point $X$ to the circle $k$ make equal angles with the lines $A X$ and $C X$.