Question 86
Let $A B C D E$ be a convex pentagon with $C D = D E$ and $\angle E D C \neq 2 \cdot \angle A D B$. Suppose that a point $P$ is located in the interior of the pentagon such that $A P = A E$ and $B P = B C$. Prove that $P$ lies on the diagonal $C E$ if and only if $\operatorname{area}(B C D) + \operatorname{area}(A D E) = \operatorname{area}(A B D) + \operatorname{area}(A B P)$.