Question 169
Let $ABC$ be a triangle, and $D, E, F$ the feet of the altitudes from $A, B, C$ respectively. Let also $H$ be the orthocentre of $ABC$, $O$ the centre of its circumcircle, and $X$ the point of the line $(EF)$ such that $XA = XD$. Show that the lines $(AX)$ and $(OH)$ are perpendicular.