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2021 AMC Fall 10A Problem 22

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2021 AMC Fall 10A Problem 22AMC 10 Step by Step
Name:                             Date: September 13, 2026
Solid Geometry · difficulty 4 of 5 · about 9 min · position P21-25

Inside a right circular cone with base radius 55 and height 1212 are three congruent spheres 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 rr ?

  1. A)

    32\frac{3}{2}

  2. B)

    90−40311\frac{90-40\sqrt{3}}{11}

  3. C)

    22

  4. D)

    144−25344\frac{144-25\sqrt{3}}{44}

  5. E)

    52\frac{5}{2}

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