MathNet 2007-part-03 — 185 problems (EN–VI) Question 25

Let $ABCDE$ be a convex pentagon with $$\angle BAC=\angle CAD=\angle DAE \quad \text{ and } \quad \angle ABC=\angle ACD=\angle ADE.$$ The diagonals $BD$ and $CE$ meet at $P$. Show that the line $AP$ meets the side $CD$ at its midpoint.