1995 AIME Problems/Problem 4
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
![[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)
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 |