MathDB

Three concentric circles have radii

3

4

, and

5

. An equilateral triangle with one vertex on each circle has side length

s

. The largest possible area of the triangle can be written as

a+\frac{b}{c}\sqrt{d}

, where

a,b,c

and

d

are positive integers,

b

and

c

are relatively prime, and

d

is not divisible by the square of any prime. Find

a+b+c+d

Problem Statement