Problem

Source: IMOTC PT2 2018 P1, 2018

Tags: geometry, circumcircle



Let $ABCD$ be a convex quadrilateral inscribed in a circle with center $O$ which does not lie on either diagonal. If the circumcentre of triangle $AOC$ lies on the line $BD$, prove that the circumcentre of triangle $BOD$ lies on the line $AC$.