Question 87
Let $ABC$ be an acute-angled triangle with $AB \lt AC$, and let points $D$ and $E$ be chosen on the sides $AC$ and $BC$ respectively in such a way that $AD = AE = AB$. The circumcircle of $ABE$ intersects the line $AC$ at $A$ and $F$ and the line $DE$ at $E$ and $P$. Prove that $P$ is the circumcentre of $BDF$.