Question 35
Let $A$, $B$, $C$, $D$ and $E$ be consecutive points on a circle with the centre at $O$, such that $|AC| = |BD| = |CE| = |DO|$. Let $H_1$, $H_2$ and $H_3$ be the orthocentres of the triangles $ACD$, $BCD$ and $BCE$. Prove that $H_1H_2H_3$ is a right triangle.