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2025 AMC 10A Problem 22

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2025 AMC 10A Problem 22AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 4 of 5 · about 7 min · position P21-25

A circle of radius rr is surrounded by three circles, whose radii are 1, 2, and 3, all externally tangent to the inner circle and externally tangent to each other, as shown in the diagram below.

figure

What is rr ?

  1. A)

    14\frac{1}{4}

  2. B)

    623\frac{6}{23}

  3. C)

    311\frac{3}{11}

  4. D)

    517\frac{5}{17}

  5. E)

    310\frac{3}{10}

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