Difference between revisions of "2014 AMC 8 Problems/Problem 20"
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| − | + | Rectangle <math>ABCD</math> has sides <math>CD=3</math> and <math>DA=5</math>. A circle of radius <math>1</math> is centered at <math>A</math>, a circle of radius <math>2</math> is centered at <math>B</math>, and a circle of radius <math>3</math> is centered at <math>C</math>. Which of the following is closest to the area of the region inside the rectangle but outside all three circles? | |
| − | + | <asy> | |
| − | + | draw((0,0)--(5,0)--(5,3)--(0,3)--(0,0)); | |
| + | draw(Circle((0,0),1)); | ||
| + | draw(Circle((0,3),2)); | ||
| + | draw(Circle((5,3),3)); | ||
| + | label("A",(0.2,0),W); | ||
| + | label("B",(0.2,2.8),NW); | ||
| + | label("C",(4.8,2.8),NE); | ||
| + | label("D",(5,0),SE); | ||
| + | label("5",(2.5,0),N); | ||
| + | label("3",(5,1.5),E); | ||
| + | </asy> | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2014|num-b=19|num-a=21}} | {{AMC8 box|year=2014|num-b=19|num-a=21}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 19:25, 26 November 2014
Rectangle 
has sides 
and 
. A circle of radius 
is centered at 
, a circle of radius 
is centered at 
, and a circle of radius 
is centered at 
. Which of the following is closest to the area of the region inside the rectangle but outside all three circles?
![[asy] draw((0,0)--(5,0)--(5,3)--(0,3)--(0,0)); draw(Circle((0,0),1)); draw(Circle((0,3),2)); draw(Circle((5,3),3)); label("A",(0.2,0),W); label("B",(0.2,2.8),NW); label("C",(4.8,2.8),NE); label("D",(5,0),SE); label("5",(2.5,0),N); label("3",(5,1.5),E); [/asy]](http://latex.artofproblemsolving.com/e/5/3/e531c5a59c1c4eec0d30c2a3e6ca52cd6bfe139a.png)
See Also
| 2014 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
