# Circles (A_{7a}) and (A_{7a}): The 2nd and 3rd rectangle circles

### Definition

The smallest circle tangent to CD and passing through the point of tangency of the common tangent of (O_{1}) and (O_{2})
to (O_{1}) is (A_{7a}). The smallest circle tangent to CD and passing through the point of tangency of the common tangent of (O_{1}) and (O_{2})
to (O_{2}) is (A_{7b}).[Dodge e.a. 1999]

### Properties

- As the points of tangency of common tangent of (O
_{1}) and (O_{2})
to (O_{1}) and (O_{2})
respectively form a rectangle together with C and D, (A_{7a}) and (A_{7a})
are symmetrics of (A_{3}).

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