Question 122
A convex pentagon $ABCDE$ is inscribed into the circle $\omega$. The diagonal $AD$ is a diameter of that circle. The diagonals $BE$ and $AC$ are perpendicular to each other. The diagonals $CE$ and $AD$ meet at point $P$. Prove that the area of the triangle $APE$ is equal to the sum of the areas of the triangles $ABC$ and $CDP$.