Lamoenian Circles of the Collinear Arbelos

For a point T and a circle δ, if two congruent circles of radius r touching at T also touch δ at points different from T , we say T generates circles of radius r with δ, and the two circles are said to be generated by T with δ. If the generated circles are Archimedean, we say T generates Archimedean circles with δ. Frank Power seems to be the earliest discoverer of this kind Archimedean circles: The farthest points on α and β from AB generate Archimedean circles with γ [6]. Let I be one of the points of intersection of γ and the radical axis of α and β. Floor van Lamoen has found that the endpoints of the diameter of the circle with diameter IO perpendicular to the line joining the centers of this circle and γ generate Archimedean circles with γ [2] (see the upper part of Figure 1). We say a circle C generates circles of radius r with δ, if the endpoints of a diameter of C generate circles of radius r with δ. Circles generating Archimedean circles with γ are said to be Lamoenian. In this article we consider those circles in a general way.