# 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 (O_{1}) and (O_{2})
is Archimedean. Similarly the circle tangent to the circle with center B through C and to the common tangent of (O_{1}) and (O_{2})
is Archimedean [van Lamoen 2006].

### Properties

- The circles (A
_{33a}) and (A_{33b}) are tangent to (O).
- The circles (A
_{33a}) and (A_{8}) are symmetric through the
point of tangency of (O_{1}) and the common tangent of (O_{1}) and (O_{2}).
This tangency point is thus point of similitude of the triple of circles
(O_{2}), (A_{33a}), and (A_{8}).

A similar result is found for (A_{33b}). [FvL, 24 Oct 2006]

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