Question 148
Let $ABC$ be an acute-angled triangle. Let point $B'$ be the reflection of $B$ across the line $AC$, and point $C'$ the reflection of $C$ across the line $AB$. The circles circumscribed about triangles $ABB'$ and $ACC'$ intersect at points $A$ and $P$. Prove that the circumcentre of triangle $ABC$ lies on the line $AP$. (Russia 2005)