Question 3
Let $ABC$ and $A'B'C'$ be two triangles having the same circumcircle $\omega$, and the same orthocentre $H$. Let $\Omega$ be the circumcircle of the triangle determined by the lines $AA'$, $BB'$, and $CC'$. Prove that $H$, the centre of $\omega$, and the centre of $\Omega$ are collinear.
(Denmark)
(Denmark)