KöMaL 2026 B5514

The sides of triangle $ABC$ satisfy $a \geq b \geq c$ (with the usual notations). Let $P$ be the endpoint of the angle bisector from point $C$ on side $AB$. Prove that the diagonals of the cyclic trapezoid with side lengths $CP$, $BP$, $CP$, $PA$ equals $\sqrt{ab}$.