TUYMAADA 2023 S4

Two points $A$ and $B$ and line $\ell$ are fixed in the plane so that $\ell$ is not perpendicular to $AB$ and does not intersect the segment $AB$ . We consider all circles with a centre $O$ not lying on $\ell$ , passing through $A$ and $B$ and meeting $\ell$ at some points $C$ and $D$ . Prove that all the circumcircles of triangles $OCD$ touch a fixed circle.