Problem

Source: Benelux Mathematical Olympiad 2015, Problem 2

Tags: geometry, circumcircle



Let ABC be an acute triangle with circumcentre O. Let ΓB be the circle through A and B that is tangent to AC, and let ΓC be the circle through A and C that is tangent to AB. An arbitrary line through A intersects ΓB again in X and ΓC again in Y. Prove that |OX|=|OY|.