IMO 2010 Shortlist G61

. The vertices X, Y , Z of an equilateral triangle XY Z lie respectively on the sides BC, CA, AB of a triangle ABC. Prov...

IMO 2010 Shortlist G61

Category: Geometry

Problem

. The vertices X, Y , Z of an equilateral triangle XY Z lie respectively on the sides BC, CA, AB of a triangle ABC. Prove that if the incenter of triangle ABC lies outside triangle XY Z, then one of the angles of triangle ABC is greater than 120. (Bulgaria)