The circumcentre O of a given cyclic quadrilateral ABCD lies inside the quadrilateral but not on the diagonal AC. The diagonals of the quadrilateral intersect at I. The circumcircle of the triangle AOI meets the sides AD and AB at points P and Q, respectively; the circumcircle of the triangle COI meets the sides CB and CD at points R and S, respectively. Prove that PQRS is a parallelogram. geometryparallelogramcircumcirclecyclic quadrilateralgeometry unsolved