Problem

Source: JBTST I , Romania, 2007

Tags: geometry, trapezoid, trigonometry, power of a point, radical axis, geometry proposed



Let $ABCD$ be a trapezium $(AB \parallel CD)$ and $M,N$ be the intersection points of the circles of diameters $AD$ and $BC$. Prove that $O \in MN$, where $O \in AC \cap BD$.