IMO 2006 Shortlist G9
Points A1,B1,C1 are chosen on the sides BC, CA, AB of a triangle ABC, respectively. The circumcircles of triangles AB1C1...
Category: Geometry
Problem
Points A1,B1,C1 are chosen on the sides BC, CA, AB of a triangle ABC, respectively. The circumcircles of triangles AB1C1, BC1A1, CA1B1 intersect the circumcircle of triangle ABC again at points A2,B2,C2, respectively (A2 6= A, B2 6= B, C2 6= C). Points A3,B3,C3 are symmetric to A1,B1,C1 with respect to the midpoints of the sides BC, CA, AB respectively. Prove that the triangles A2B2C2 and A3B3C3 are similar. (Russia)