Let D be a point on the side BC of an equilateral triangle ABC where D is different than the vertices. Let I be the excenter of the triangle ABD opposite to the side AB and J be the excenter of the triangle ACD opposite to the side AC. Let E be the second intersection point of the circumcircles of triangles AIB and AJC. Prove that A is the incenter of the triangle IEJ. geometryincentercircumcirclegeometry proposed