Circles (A24a), (A24b), (A24c), and (A24d): The Power circles

Definition

Let M1 and M2 be the midpoints of arcs (O1) and (O2) respectively. The four circles tangent to OM1 and OM2 and also tangent to (O) are Archimedean. [Power, 2005]

Powerian Pairs

After these two pairs of Archimedean circles, we call pairs of Archimedean circles tangent to each other in a given point and tangent to a given circle Powerian pairs. [van Lamoen, 2007]

Generalization

These circles have been generalized considerably by Hiroshi Okumura in 2013, see Circles (A38a), (A38b), (A38c), and (A38d): The CD-circle Powerian Pairs


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