Question 9
B3 (GBR 1). Let $ABC$ be a triangle, and let $P$ be a point inside it such that $\angle PAC=\angle PBC$. The perpendiculars from $P$ to $BC$ and $CA$ meet these lines at $L$ and $M$, respectively, and $D$ is the midpoint of $AB$. Prove that $DL=DM$.