Question 87
In a quadrilateral $ABCD$ we have $\angle BAD = 110^\circ$, $\angle CBA = 50^\circ$, $\angle DCB = 70^\circ$. Let $M$ and $N$ be the midpoints of segments $\overline{AB}$ and $\overline{CD}$ respectively. Let $P$ be a point on the segment $\overline{MN}$ such that $|AM| : |CN| = |MP| : |NP|$ and $|AP| = |CP|$. Determine $\angle CPA$.