Problem

Source: Indian IMOTC 2013, Practice Test 1, Problem 2

Tags: geometry, circumcircle, trigonometry, cyclic quadrilateral, perpendicular bisector, geometry proposed



Let $ABCD$ by a cyclic quadrilateral with circumcenter $O$. Let $P$ be the point of intersection of the diagonals $AC$ and $BD$, and $K, L, M, N$ the circumcenters of triangles $AOP, BOP$, $COP, DOP$, respectively. Prove that $KL = MN$.