MathDB

We have

3

circles such that any

2

of them are externally tangent. Let

a

be length of the outer tangent common to a pair of them. The lengths

b

and

c

are defined similarly. If

T

is the sum of the areas of such circles, show that

\pi (a + b + c)^2 \le 12T

.
Note: In In the case of externally tangent circles, the common external tangent is the segment tangent to them that touches them at different points.

Problem Statement