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Circumcenter of AJ_bJ_c lies on A-bisector

Source: RMM 2015 Problem 4

March 1, 2015
geometrygeometry proposed

Problem Statement

Let ABCABC be a triangle, and let DD be the point where the incircle meets side BCBC. Let JbJ_b and JcJ_c be the incentres of the triangles ABDABD and ACDACD, respectively. Prove that the circumcentre of the triangle AJbJcAJ_bJ_c lies on the angle bisector of ∠BAC\angle BAC.
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