Circles (A_33a) and (A_33b): Brothers of the quadruplet circle

Definition

The circle tangent to the circle with center A through C and to the common tangent of (O₁) and (O₂) is Archimedean. Similarly the circle tangent to the circle with center B through C and to the common tangent of (O₁) and (O₂) is Archimedean [van Lamoen 2006].

Properties

• The circles (A_33a) and (A_33b) are tangent to (O).
• The circles (A_33a) and (A₈) are symmetric through the point of tangency of (O₁) and the common tangent of (O₁) and (O₂). This tangency point is thus point of similitude of the triple of circles  (O₂), (A_33a), and (A₈).
  
  A similar result is found for (A_33b). [FvL, 24 Oct 2006]

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