Create a circle tangent to three existing circles.

Input parameters:

1. Ca → First tangent circle.
2. Cb → Second tangent circle.
3. Cc → Third tangent circle.
4. Ia → Inside or outside state of the first tangent circle.
   •  True → Interior
   • False → Exterior
5. Ib → Inside or outside state of the second tangent circle.
   •  True → Interior
   • False → Exterior
6. Ic → Inside or outside state of the third tangent circle.
   •  True → Interior
   • False → Exterior

Output parameters:

1. Ci → Apollonian circle.