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 the value of $a+b+c+d$? $\textbf{(A) } 119 \qquad$ $ \textbf{(B) } 120 \qquad$ $ \textbf{(C) } 121 \qquad$ $ \textbf{(D) } 122 \qquad$ $ \textbf{(E) } 123 \qquad$