Difference between revisions of "1995 AIME Problems/Problem 4"
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== Problem == | == Problem == | ||
| − | Circles of radius <math> | + | Circles of radius <math>3</math> and <math>6</math> are externally tangent to each other and are internally tangent to a circle of radius <math>9</math>. The circle of radius <math>9</math> has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord. |
| + | |||
| + | <center><asy> | ||
| + | size(200); | ||
| + | pair A=(0,0), B=(3,0), C=(-6,0); | ||
| + | draw(Circle(A,9)); | ||
| + | draw(Circle(B,3)); | ||
| + | draw(Circle(C,6)); | ||
| + | </asy></center> | ||
== Solution == | == Solution == | ||
| + | <center><asy> | ||
| + | size(200); | ||
| + | pair A=(0,0), B=(3,0), C=(-6,0); | ||
| + | draw(Circle(A,9)); | ||
| + | draw(Circle(B,3)); | ||
| + | draw(Circle(C,6)); | ||
| + | </asy></center> | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=1995|num-b=3|num-a=5}} | |
| − | + | ||
| − | + | [[Category:Intermediate Geometry Problems]] | |
Revision as of 14:59, 15 March 2008
Problem
Circles of radius 
and 
are externally tangent to each other and are internally tangent to a circle of radius 
. The circle of radius has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.
![[asy] size(200); pair A=(0,0), B=(3,0), C=(-6,0); draw(Circle(A,9)); draw(Circle(B,3)); draw(Circle(C,6)); [/asy]](http://latex.artofproblemsolving.com/5/c/a/5cad59211f290007f7b96b59b377b5b49c3611de.png)
Solution
See also
| 1995 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
