Given a triangle $ABC$ with incenter $I$ . It is known that $E_A$ is center of the ex-circle tangent to $BC$. Likewise, $E_B$ and $E_C$ are the centers of the ex-circles tangent to $AC$ and $AB$, respectively. Prove that $I$ is the orthocenter of the triangle $E_AE_BE_C$.
Problem
Source: Indonesia INAMO Shortlist 2009 G10 https://artofproblemsolving.com/community/c1101409_
Tags: geometry, incenter, excircles, excenters