If a cyclic quadrilateral is inscribed in a circle of a coaxal system such that one pair of connectors touches another circle of the system at , then each pair of opposite connectors will touch a circle of the system ( at on , at on , at on , at on , and at on ), and the six points of contact , , , , , and will be collinear.
The general theorem states that if , , ..., are any number of points taken in order on a circle of a given coaxal system so that , , ..., touch respectively fixed circles , , ..., of the system, then must touch a fixed circle of the system. Further, if , , ..., touch respectively any of the circles , , ..., , then must touch the remaining circle.