Question 72
In an equilateral triangle $ABC$, let $D$ be a point on the side $[BC]$ other 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 the circumcircles of the triangles $AIB$ and $AJC$ intersect at the point $E$ for the second time. Prove that $A$ is the incenter of the triangle $IEJ$.