Assume circle contains circle . If it is possible to inscribe a quadrilateral touching with its vertices and with its sides, then it is always possible to find a quadrilateral touching both circles and passing through any point of outside . Such quadrilaterals are called bicentric. For this Demonstration circle (in tan) is fixed and the position of circle (in brown) can be changed by dragging the red center (the radius of is obtained through Fuss's formula). You can change the position of the red vertex of the quadrilateral.