Difference between revisions of "2024 AMC 10A Problems/Problem 14"
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| + | == Problem == | ||
| + | One side of an equilateral triangle of height <math>24</math> lies on line <math>\ell</math>. A circle of radius <math>12</math> is tangent to line <math>\ | ||
| + | ell</math> 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 <math>\ell</math> can be written as <math>a \sqrt{b} - c \pi</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are positive integers and <math>b</math> is not divisible by the square of any prime. What is <math>a + b + c</math>? | ||
| + | |||
| + | <math>\textbf{(A)}~72\qquad\textbf{(B)}~73\qquad\textbf{(C)}~74\qquad\textbf{(D)}~75\qquad\textbf{(E)}~76</math> | ||
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| + | == Diagram == | ||
Revision as of 17:34, 8 November 2024
Problem
One side of an equilateral triangle of height 
lies on line 
. A circle of radius 
is tangent to line 
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 can be written as 
, where 
, 
, and 
are positive integers and is not divisible by the square of any prime. What is 
?
