Question 151
Let $ABC$ be a triangle and let $I_A$, $I_B$, $I_C$ be centers of the excircles tangent to its sides $BC$, $CA$, $AB$, respectively. Denote by $X$, $Y$, $Z$ the orthocenters of triangles $I_ABC$, $AI_BC$, $ABI_C$, respectively. Prove that the triangles $ABC$ and $XYZ$ are congruent. (Michal Janík)