Question 18
Let $I$ be the incentre of triangle $ABC$ and $J$ the excentre opposite $A$. Let $\overline{AA'}$ be a diameter of the circumcircle of $\triangle ABC$, and let $H_1, H_2$ be the orthocentres of $\triangle BIA'$ and $\triangle CJA'$, respectively. Prove that $H_1H_2$ is parallel to $BC$.