IMO 2010 Shortlist G6

The vertices X, Y , Z of an equilateral triangle XY Z lie respectively on the sides BC, CA, AB of an acute-angled triang...

IMO 2010 Shortlist G6

Category: Geometry

Problem

The vertices X, Y , Z of an equilateral triangle XY Z lie respectively on the sides BC, CA, AB of an acute-angled triangle ABC. Prove that the incenter of triangle ABC lies inside triangle XY Z.