IMO 2009 Shortlist G7

Let ABC be a triangle with incenter I and let X, Y and Z be the incenters of the triangles BIC, CIA and AIB, respectivel...

imomathematicsolympiadshortlistgeometry

IMO 2009 Shortlist G7

Category: Geometry

Problem

Let ABC be a triangle with incenter I and let X, Y and Z be the incenters of the triangles BIC, CIA and AIB, respectively. Let the triangle XY Z be equilateral. Prove that ABC is equilateral too.