Difference between revisions of "2011 AMC 10A Problems/Problem 18"
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<math> \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{(B)}\ 1 + \frac{\pi}{2} </math> | <math> \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{(B)}\ 1 + \frac{\pi}{2} </math> | ||
+ | [[Category: Introductory Geometry Problems]] | ||
== Solution == | == Solution == |
Revision as of 10:42, 13 August 2014
Problem 18
Circles and
each have radius 1. Circles
and
share one point of tangency. Circle
has a point of tangency with the midpoint of
. What is the area inside Circle
but outside circle
and circle
?
Solution
Draw a rectangle with vertices at the centers of and
and the intersection of
and
. Then, we can compute the shaded area as the area of half of
plus the area of the rectangle minus the area of the two sectors created by
and
. This is
.
See Also
2011 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.