Let $ABCD$ be a convex quadrilateral and draw regular triangles $ABM, CDP, BCN, ADQ$, the first two outward and the other two inward. Prove that $MN = AC$. What can be said about the quadrilateral $MNPQ$?
Problem
Source: IMO LongList 1982 - P45
Tags: symmetry, geometry, IMO Longlist, convex quadrilateral, IMO Shortlist