




And the area between the 3 tangent circles (green area) is:
A = A_{T} − A_{A} − A_{B} − A_{C}
The angles of the triangle ABC can be found by cosine law:


And the curvature of the circles k_{4} and k_{5} which are called the Soddy circles are:



NOTE: in all the calculations we assumed that r_{2} > r_{3}
