AMC 10A 2025 (Problem 20)

A silo (right circular cylinder) with diameter

20

meters stands in a field. MacDonald is located

20

meters west and

15

meters south of the center of the silo. McGregor is located

20

meters east and

g>0

meters south of the center of the silo. The line of sight between MacDonald and McGregor is tangent to the silo. The value of

g

can be written as

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

, where

a

b

c

, and

d

are positive integers,

b

is not divisible by the square of any prime, and

d

is relatively prime to the greatest common divisor of

a

and

c

. What is

a+b+c+d

\text{(A)}\;119

\text{(B)}\;120

\text{(C)}\;121

\text{(D)}\;122

\text{(E)}\;123