Problem

Source: Saudi Arabia IMO TST Day IV Problem 4

Tags: geometry, circumcircle, incenter, geometric transformation, reflection, perpendicular bisector, angle bisector



Points A1, B1, C1 lie on the sides BC, AC and AB of a triangle ABC, respectively, such that AB1AC1=CA1CB1=BC1BA1. Let IA, IB, IC be the incenters of triangles AB1C1, A1BC1 and A1B1C respectively. Prove that the circumcenter of triangle IAIBIC, is the incenter of triangle ABC.