MathDB

Let

C_1, C_2

and

C_3

be three circles, of radii

2, 4

and

6

respectively. It is known that each of them are tangent exteriorly with the other two circles. Let

\Omega_1

and

\Omega_2

be two more circles, each of them tangent to all of the

3

circles above, of radius

\omega_1

and

\omega_2

respectively. Prove that

\omega_1 + \omega_2 = 2\omega_1\omega_2

6.3