Circle (A₈): The 4th rectangle circle

Definition

The smallest circle tangent to the common tangent of (O₁) and (O₂) trhough C is (A₈). [Dodge e.a. 1999]

Properties

• Cf. (A_7a) and (A_7b).
• The center of (A₈) lies on the Schoch line (see the Schoch incircle) [Okumura and Watanabe 2004].
• The point of tangency of (O₁) and the common tangent of (O₁) and (O₂) is the external center of similitude of (A₈) and (O₂). Similarly the point of tangency of (O₂) and the common tangent of (O₁) and (O₂) is the external center of similitude of (A₈) and (O₁). [Okumura and Watanabe 2004].
  
• See also Brothers of the quadruplet circle.

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