If AC, BD, EF are the diagonals of the quadrilateral and PQR is the triangle formed by the diagonals, the circles on the diagonals as diameters form a co-axal system and the circle PQR is a circle of the complementary system. If the circles on the diagonals as diameters intersect in real points S1, S2, then S1, S2 are the limiting points of the system to which the circle PQR belongs and if S1, S2 are not real points and if the straight line joining the mid-points of the diagonals cuts the circle PQR in L1, L2 then all the circles of the system to which the circle PQR belongs pass through L1, L2 and L1, L2 are the limiting points of the system to which the circles on the diagonals as diameters belong.