2024 AMC 10A Problem 14

One side of an equilateral triangle of height

24

lies on line

\ell

. A circle of radius

12

is tangent to line

\ell

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

\ell

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

\text{(A)}\;72

\text{(B)}\;73

\text{(C)}\;74

\text{(D)}\;75

\text{(E)}\;76