Question 89
Let $ABC$ be a right-angled triangle with $\angle B = 90^{\circ}$. Let $BD$ be the altitude from $B$ onto $AC$. Let $P$, $Q$ and $I$ be the incentres of triangles $ABD$, $CBD$ and $ABC$ respectively. Show that the circumcentre of the triangle $PIQ$ lies on the hypotenuse $AC$.