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2021 Fall AMC 10A Problems/Problem 22

Revision as of 19:12, 22 November 2021 by Leo.euler (talk | contribs) (Created page with "== Problem == Inside a right circular cone with base radius <math>5</math> and height <math>12</math> are three congruent spheres with radius <math>r</math>. Each sphere is ta...")
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Problem

Inside a right circular cone with base radius $5$ and height $12$ are three congruent spheres with radius $r$. Each sphere is tangent to the other two spheres and also tangent to the base and side of the cone. What is $r$?

$\textbf{(A)}\ \frac{3}{2} \qquad\textbf{(B)}\ \frac{90-40\sqrt{3}}{11} \qquad\textbf{(C)}\ 2 \qquad\textbf{(D)}\ \frac{144-25\sqrt{3}}{44} \qquad\textbf{(E)}\ \frac{5}{2}$

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