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2003 AMC 10B Problem 19

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2003 AMC 10B Problem 19AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 3 of 5 · about 5 min · position P16-20

Three semicircles of radius 11 are constructed on diameter AB‾\overline{AB} of a semicircle of radius 22 . The centers of the small semicircles divide AB‾\overline{AB} into four line segments of equal length, as shown. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicircles?

figure

  1. A)

    π−3\pi - \sqrt{3}

  2. B)

    π−2\pi - \sqrt{2}

  3. C)

    π+22\frac{\pi + \sqrt{2}}{2}

  4. D)

    π+32\frac{\pi +\sqrt{3}}{2}

  5. E)

    76π−32\frac{7}{6}\pi - \frac{\sqrt{3}}{2}

Working