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Equilateral triangle and incenter

Source: Turkey JBMO Team Selection Test 2013, P1

May 31, 2013
geometryincentercircumcirclegeometry proposed

Problem Statement

Let DD be a point on the side BCBC of an equilateral triangle ABCABC where DD is different than the vertices. Let II be the excenter of the triangle ABDABD opposite to the side ABAB and JJ be the excenter of the triangle ACDACD opposite to the side ACAC. Let EE be the second intersection point of the circumcircles of triangles AIBAIB and AJCAJC. Prove that AA is the incenter of the triangle IEJIEJ.
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