MathDB

Three mutually externally tangent circles are internally tangent to a circle with radius

1

. If two of the inner circles have radius

\frac{1}{3}

, the largest possible radius of the third inner circle can be expressed in the form

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

where

c

is squarefree and

\gcd(a,b,d)=1

. Find

a+b+c+d

Problem Statement