2025 AMC 10A 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 \gt 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 \dfrac{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?

\textbf{(A)} 119 \qquad \textbf{(B)} 120 \qquad \textbf{(C)} 121 \qquad \textbf{(D)} 122 \qquad \textbf{(E)} 123

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.