MEMO 2022 Problem 6

Let $ABCD$ be a convex quadrilateral such that $AC = BD$ and the sides $AB$ and $CD$ are not parallel. Let $P$ be the intersection point of the diagonals $AC$ and $BD$ . Points $E$ and $F$ lie, respectively, on segments $BP$ and $AP$ such that $PC=PE$ and $PD=PF$ . Prove that the circumcircle of the triangle determined by the lines $AB, CD, EF$ is tangent to the circumcircle of the triangle $ABP$ .