2025 AMC 10A Problems/Problem 20: Difference between revisions
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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 <imath>g > 0</imath> meters south of the center of the silo. The light of sight between MacDonald and McGregor is tangent to the silo. The value of g can be written as <imath>\frac{a\sqrt{b}-c}{d}</imath>, where <imath>a,b,c,</imath> and <imath>d</imath> are positive integers, <imath>b</imath> is not divisible by the square of any prime, and <imath>d</imath> is relatively prime to the greatest common divisor of <imath>a</imath> and <imath>c</imath>. What is <imath>a+b+c+d</imath>? | |||
<imath>\textbf{(A) } 118 \qquad\textbf{(B) } 119 \qquad\textbf{(C) } 120 \qquad\textbf{(D) } 121 \qquad\textbf{(E) } 122</imath> | |||
=Solution 1= | |||
Revision as of 14:50, 6 November 2025
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 
meters south of the center of the silo. The light of sight between MacDonald and McGregor is tangent to the silo. The value of g can be written as 
, where 
and 
are positive integers, 
is not divisible by the square of any prime, and is relatively prime to the greatest common divisor of 
and 
. What is 
?
