Locus, maybe nice problem

[nvhhnvn]

Let $ABCD$ be inscribed in circle $(O)$. Denote $T=AB\cap CD$. Let $M$ be a point that moving on the line $CD$. Denote $(O_1)\equiv (MAD), (O_2)\equiv (MBC), (O_3)\equiv (MBD), (O_4)\equiv (MAC)$. $S=O_1O_2\cap O_3O_4$. Find the locus of $S$.