# Circle (A_{8}): The 4th rectangle circle

### Definition

The smallest circle tangent to the common tangent of (O_{1}) and (O_{2})
trhough C is (A_{8}). [Dodge e.a. 1999]

### Properties

- Cf. (A
_{7a}) and (A_{7b}).
- The center of (A
_{8}) lies on the Schoch line (see
the Schoch incircle) [Okumura and
Watanabe 2004].
- The point of tangency of (O
_{1}) and the common tangent of (O_{1}) and (O_{2})
is the external center of similitude of (A_{8}) and (O_{2}).
Similarly the point of tangency of (O_{2}) and the common tangent of
(O_{1}) and (O_{2})
is the external center of similitude of (A_{8}) and (O_{1}).
[Okumura and Watanabe 2004].

- See also Brothers of the quadruplet circle.
- This is a special case of the third generalization mentioned at Bankoff's Triplet circle

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