MathNet 2016-part-01 — 184 problems (EN–VI) Question 83

Let $ABCD$ be a cyclic quadrilateral. Let $M$ be the midpoint of $CD$. Let $P$ be a point inside $ABCD$ such that $PA = PB = CM$. Prove that $AB$, $CD$, and the perpendicular bisector of $MP$ are concurrent or parallel.