Problem

Source: ELMO 2014 Shortlist G1, by Sammy Luo

Tags: geometry, circumcircle, Asymptote, geometric transformation, homothety, blogs, conics



Let ABC be a triangle with symmedian point K. Select a point A1 on line BC such that the lines AB, AC, A1K and BC are the sides of a cyclic quadrilateral. Define B1 and C1 similarly. Prove that A1, B1, and C1 are collinear. Proposed by Sammy Luo