Question 140
One side of an equilateral triangle of height $24$ lies on line $l$. A circle of radius $12$ is tangent to $l$ and is externally tangent to the triangle. The area of the region exterior to the triangle and the circle and bounded by the triangle, the circle, and line $l$ can be written as $a\sqrt{b} - c\pi$, where $a$, $b$, and $c$ are positive integers and $b$ is not divisible by the square of any prime. What is $a + b + c$?
(A) 72 (B) 73 (C) 74 (D) 75 (E) 76
(A) 72 (B) 73 (C) 74 (D) 75 (E) 76