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2019 AMC 10A Problem 16

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2019 AMC 10A Problem 16AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 3 of 5 · about 4 min · position P16-20

The figure below shows 1313 circles of radius 11 within a larger circle. All the intersections occur at points of tangency. What is the area of the region, shaded in the figure, inside the larger circle but outside all the circles of radius 1?1 ?

figure

  1. A)

    4π34 \pi \sqrt{3}

  2. B)

    7π7 \pi

  3. C)

    π(33+2)\pi\left(3\sqrt{3} +2\right)

  4. D)

    10π(3−1)10 \pi \left(\sqrt{3} - 1\right)

  5. E)

    π(3+6)\pi\left(\sqrt{3} + 6\right)

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