AMC 10A 2025 (Problem 22)

Coordinate GeometryVery Hard

A circle of radius

r

is surrounded by three circles, whose radii are

1

2

, and

3

, all externally tangent to the inner circle and externally tangent to each other, as shown below. What is

r

\text{(A)}\;\frac{1}{4}

\text{(B)}\;\frac{6}{23}

\text{(C)}\;\frac{3}{11}

\text{(D)}\;\frac{5}{17}

\text{(E)}\;\frac{3}{10}