Question 85
Let $ABC$ be an acute triangle and let $H$ be its orthocenter. Let $G$ be the intersection of the parallel to $AB$ through $H$ with the parallel to $AH$ through $B$. Let $I$ be the point on the line $GH$ such that $AC$ cuts the segment $HI$ at its midpoint. Let $J$ be the second intersection of $AC$ with the circumcircle of the triangle $CGI$. Show that $IJ = AH$.
