Question 52
Let $\triangle ABC$ be a triangle with $m(\angle ABC) = 75^\circ$ and $m(\angle ACB) = 45^\circ$. The angle bisector of $\angle CAB$ intersects $CB$ at the point $D$. We consider the point $E \in (AB)$ such that $DE = DC$. Let $P$ be the intersection of the lines $AD$ and $CE$. Prove that $P$ is the midpoint of the segment $AD$.