# Circle (A_{6}): The C-circle

### Definition

The circle centered at C tangent to the tangents from O_{1} to (O_{2}) and from O_{2}
to (O_{1}). [Dodge e.a 1999]

### Properties

- A
_{5a}A_{5b} is a diameter of (A_{6}).
- Let the tangent from O
_{1} to (O_{2}) cut a diameter XY
off (O_{1}), and meet (O_{2}) in U. Let UZ be a diameter of (O_{2}).
Then (A_{6}) is the incircle of the insquare inscribed in triangle
XYZ with one side of the square coinciding with XY.

A similar construction can be found from the tangent from O_{2}
to (O_{1})

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