# Three Circles with Two Common Tangents

Three Circles with Two Common Tangents

Let be a triangle circumscribed by the circle . Let be a point on ; form the line . Consider three other circles , , and with the common tangent , with inscribed in the triangle , and and tangent to both the segment and . Prove that , , and have two common tangents.

ABC

γ

D

AB

CD

γ

1

γ

2

γ

3

AB

γ

1

ABC

γ

2

γ

3

CD

γ

γ

1

γ

2

γ

3