Difference between revisions of "2017 AMC 12A Problems/Problem 16"
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\qquad\textbf{(D)}\ \frac{5}{8}\sqrt{2} | \qquad\textbf{(D)}\ \frac{5}{8}\sqrt{2} | ||
\qquad\textbf{(E)}\ \frac{11}{12} </math> | \qquad\textbf{(E)}\ \frac{11}{12} </math> | ||
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| + | ==Solution== | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC12 box|year=2017|ab=A|num-b=15|num-a=17}} | ||
| + | {{MAA Notice}} | ||
Revision as of 17:52, 8 February 2017
Problem
In the figure below, semicircles with centers at 
and 
and with radii 2 and 1, respectively, are drawn in the interior of, and sharing bases with, a semicircle with diameter 
. The two smaller semicircles are externally tangent to each other and internally tangent to the largest semicircle. A circle centered at 
is drawn externally tangent to the two smaller semicircles and internally tangent to the largest semicircle. What is the radius of the circle centered at ?
![[asy] size(5cm); draw(arc((0,0),3,0,180)); draw(arc((2,0),1,0,180)); draw(arc((-1,0),2,0,180)); draw((-3,0)--(3,0)); pair P = (-1,0)+(2+6/7)*dir(36.86989); draw(circle(P,6/7)); dot((-1,0)); dot((2,0)); dot(P); [/asy]](http://latex.artofproblemsolving.com/c/7/0/c70afdd05a6954478364e08a7b13089dc5022e4a.png)
Solution
See Also
| 2017 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 15 |
Followed by Problem 17 |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
