Question 66
Let $ABCD$ be a convex quadrilateral such as $AC = BD$ and such that the sides $AB$ and $CD$ are not parallel. Let $P$ be the point of intersection of the diagonal $(AC)$ and $(BD)$. Let $E$ and $F$ points respectively on the segments $[BP]$ and $[AP]$ such as $PC = PE$ and $PD = PF$. Show that the circle circumscribes to the triangle formed by the lines $(AB)$, $(CD)$ and $(EF)$ is tangent to the circle circumscribed with the triangle $ABP$.