Question 23
(GBR) Let $ABCD$ be a convex quadrilateral and $O$ the intersection of its diagonals $AC$ and $BD$. If
$$OA\sin\angle A+OC\sin\angle C=OB\sin\angle B+OD\sin\angle D,$$
prove that $ABCD$ is cyclic.
$$OA\sin\angle A+OC\sin\angle C=OB\sin\angle B+OD\sin\angle D,$$
prove that $ABCD$ is cyclic.