Let three circles Γ1,Γ2,Γ3, which are non-overlapping and mutually external, be given in the plane. For each point P in the plane, outside the three circles, construct six points A1,B1,A2,B2,A3,B3 as follows: For each i \equal{} 1, 2, 3, Ai,Bi are distinct points on the circle Γi such that the lines PAi and PBi are both tangents to Γi. Call the point P exceptional if, from the construction, three lines A1B1,A2B2,A3B3 are concurrent. Show that every exceptional point of the plane, if exists, lies on the same circle. radical axisgeometry unsolvedgeometry