Question 40
Let $H$ be the orthocenter of an acute triangle $ABC$. (The orthocenter is the point at the intersection of the three altitudes. An acute triangle has all angles less than $90^{\circ}$.) Draw three circles: one passing through $A$, $B$ and $H$, another passing through $B$, $C$ and $H$, and finally, one passing through $C$, $A$ and $H$. Prove that the triangle whose vertices are the centers of those three circles is congruent to triangle $ABC$.