MathDB
IMO Shortlist 2009 - Problem G7

Source:

July 5, 2010
geometryincenterreflectioninequalitiesIMO Shortlist

Problem Statement

Let ABCABC be a triangle with incenter II and let XX, YY and ZZ be the incenters of the triangles BICBIC, CIACIA and AIBAIB, respectively. Let the triangle XYZXYZ be equilateral. Prove that ABCABC is equilateral too.
Proposed by Mirsaleh Bahavarnia, Iran
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