PAMO 2021 Problem 6

Let $ABCD$ be a trapezoid which is not a parallelogram, such that $AD$ is parallel to $BC$ . Let $O=BD\cap AC$ and $S$ be the second intersection of the circumcircles of triangles $AOB$ and $DOC$ . Prove that the circumcircles of triangles $ASD$ and $BSC$ are tangent.