Problem

Source: 2021 Junior Macedonian Mathematical Olympiad P2

Tags: geometry



Let $ABCD$ be a tangential quadrilateral with inscribed circle $k(O,r)$ which is tangent to the sides $BC$ and $AD$ at $K$ and $L$, respectively. Show that the circle with diameter $OC$ passes through the intersection point of $KL$ and $OD$. Proposed by Ilija Jovchevski