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2007 AMC 10A Problem 24

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2007 AMC 10A Problem 24AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 4 of 5 · about 5 min · position P21-25

Circles centered at AA and BB each have radius 22 , as shown. Point OO is the midpoint of AB‾\overline{AB} , and OA=22OA = 2\sqrt {2} . Segments OCOC and ODOD are tangent to the circles centered at AA and BB , respectively, and EFEF is a common tangent. What is the area of the shaded region ECODFECODF ?

figure

  1. A)

    823\frac {8\sqrt {2}}{3}

  2. B)

    82−4−π8\sqrt {2} - 4 - \pi

  3. C)

    424\sqrt {2}

  4. D)

    42+π84\sqrt {2} + \frac {\pi}{8}

  5. E)

    82−2−π28\sqrt {2} - 2 - \frac {\pi}{2}

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