MathDB
coneblocked 2.0

Source: 2021 AMC 10A #22

November 11, 2021

Problem Statement

Inside a right circular cone with base radius 55 and height 1212 are three congruent spheres each with radius rr. Each sphere is tangent to the other two spheres and also tangent to the base and side of the cone. What is r?r?
<spanclass=latexbold>(A)</span>32<spanclass=latexbold>(B)</span>9040311<spanclass=latexbold>(C)</span>2<spanclass=latexbold>(D)</span>14425344<spanclass=latexbold>(E)</span>52<span class='latex-bold'>(A) </span>\dfrac32\qquad<span class='latex-bold'>(B) </span>\dfrac{90 - 40\sqrt3}{11}\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>\dfrac{144 - 25\sqrt3}{44}\qquad<span class='latex-bold'>(E) </span>\dfrac52