Question 99
Let $ABC$ be a triangle, with $AB \lt AC$, $D$ the foot of the altitude from $A$, $M$ the midpoint of $BC$, and $B'$ the symmetric of $B$ with respect to $D$. The perpendicular line to $BC$ at $B'$ intersects $AC$ at point $P$. Prove that if $BP$ and $AM$ are perpendicular then triangle $ABC$ is right-angled.