Difference between revisions of "2007 AMC 10A Problems/Problem 24"

(New page: ==Problem== Circles centered at <math>A</math> and <math>B</math> each have radius <math>2</math>, as shown. Point <math>O</math> is the midpoint of <math>\overline{AB}</math>, and <math>O...)
 
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{{AMC10 box|year=2007|ab=A|num-b=23|num-a=25}}
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[[Category:Introductory Geometry Problems]]

Revision as of 11:34, 5 February 2008

Problem

Circles centered at $A$ and $B$ each have radius $2$, as shown. Point $O$ is the midpoint of $\overline{AB}$, and $OA = 2\sqrt {2}$. Segments $OC$ and $OD$ are tangent to the circles centered at $A$ and $B$, respectively, and $EF$ is a common tangent. What is the area of the shaded region $ECODF$?


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$\text{(A)}\ \frac {8\sqrt {2}}{3} \qquad \text{(B)}\ 8\sqrt {2} - 4 - \pi \qquad \text{(C)}\ 4\sqrt {2} \qquad \text{(D)}\ 4\sqrt {2} + \frac {\pi}{8} \qquad \text{(E)}\ 8\sqrt {2} - 2 - \frac {\pi}{2}$

Solution

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See also

2007 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 23
Followed by
Problem 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions