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2014 AMC 10B Problem 22

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2014 AMC 10B Problem 22AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 4 of 5 · about 4 min · position P21-25

Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles?

figure

  1. A)

    1+24\dfrac{1+\sqrt2}4

  2. B)

    5−12\dfrac{\sqrt5-1}2

  3. C)

    3+14\dfrac{\sqrt3+1}4

  4. D)

    235\dfrac{2\sqrt3}5

  5. E)

    53\dfrac{\sqrt5}3

Working