Question 35
Let $ABC$ be a triangle with $BC = 1$ and angle $BAC$ acute. Let $D$ be the intersection of the internal bisector of angle $BAC$ with side $BC$, $H$ the orthocentre and $O$ the circumcentre of $ABC$. Find the value of $AB:AC$ in the case that $HOCB$ and $AHDO$ are cyclic.