Difference between revisions of "2011 AMC 12A Problems/Problem 11"

(Problem)
(Solution)
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== Solution ==
 
== Solution ==
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D
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== See also ==
 
== See also ==
 
{{AMC12 box|year=2011|num-b=10|num-a=12|ab=A}}
 
{{AMC12 box|year=2011|num-b=10|num-a=12|ab=A}}

Revision as of 19:15, 18 February 2011

Problem

Circles $A, B,$ and $C$ each have radius 1. Circles $A$ and $B$ share one point of tangency. Circle $C$ has a point of tangency with the midpoint of $\overline{AB}.$ What is the area inside circle $C$ but outside circle $A$ and circle $B?$

$\textbf{(A)}\ 3 - \frac{\pi}{2} \qquad \textbf{(B)}\ \frac{\pi}{2} \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ \frac{3\pi}{4} \qquad \textbf{(E)}\ 1+\frac{\pi}{2}}$ (Error compiling LaTeX. Unknown error_msg)

Solution

D

See also

2011 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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 12 Problems and Solutions