AMC 10 Step by Step
Log inSign up
Printable

2012 AMC 10A Problem 18

Include the solutionBack to the problem
2012 AMC 10A Problem 18AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 3 of 5 · about 5 min · position P16-20

The closed curve in the figure is made up of 99 congruent circular arcs each of length 2π3\frac{2\pi}{3} , where each of the centers of the corresponding circles is among the vertices of a regular hexagon of side 22 . What is the area enclosed by the curve?

figure

  1. A)

    2π+62\pi+6

  2. B)

    2π+432\pi+4\sqrt{3}

  3. C)

    3π+43\pi+4

  4. D)

    2π+33+22\pi+3\sqrt{3}+2

  5. E)

    π+63\pi+6\sqrt{3}

Working