Extensions of opposite sides of a convex quadrilateral ABCD intersect at points P and Q. Points are marked on the sides of ABCD (one per side), which are the vertices of a parallelogram with a side parallel to PQ. Prove that the intersection point of the diagonals of this parallelogram lies on one of the diagonals of quadrilateral ABCD. (E. Bakaev)
Problem
Source: 2022 Oral Moscow Geometry Olympiad grades 10-11 p3
Tags: geometry, parallelogram, collinear