Question 14
G8 (COL). Let $ABC$ be a triangle. A circle passing through $B$ and $C$ intersects the sides $AB$ and $AC$ again at $C'$ and $B'$, respectively. Prove that $BB'$, $CC'$, and $HH'$ are concurrent, where $H$ and $H'$ are the orthocenters of triangles $ABC$ and $AB'C'$ respectively.