Let us make a the radius of the largest circle centre A etc. Then the lengths of the sides of the triangle are: AB = a - b, AC = a - c and BC = b + c.

The perimeter of the triangle is:

AB + BC + CA = (a - b) + (a - c) + (b + c) = 2a.

So the perimeter of the triangle is twice the radius of the large circle whatever the sizes of the small circles.