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2004 AMC 10B Problem 25

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2004 AMC 10B Problem 25AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 4 of 5 · about 7 min · position P21-25

A circle of radius 11 is internally tangent to two circles of radius 22 at points AA and BB , where ABAB is a diameter of the smaller circle. What is the area of the region, shaded in the picture, that is outside the smaller circle and inside each of the two larger circles?

figure

  1. A)

    53π−32\frac{5}{3} \pi - 3\sqrt 2

  2. B)

    53π−23\frac{5}{3} \pi - 2\sqrt 3

  3. C)

    83π−33\frac{8}{3} \pi - 3\sqrt 3

  4. D)

    83π−32\frac{8}{3} \pi - 3\sqrt 2

  5. E)

    83π−23\frac{8}{3} \pi - 2\sqrt 3

Working