1995 AIME Problems/Problem 4

Problem

Circles of radius $3$ and $6$ are externally tangent to each other and are internally tangent to a circle of radius $9$ . The circle of radius $9$ has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.

$[asy] size(200); pair A=(0,0), B=(3,0), C=(-6,0); draw(Circle(A,9)); draw(Circle(B,3)); draw(Circle(C,6)); [/asy]$

Solution

$[asy] size(200); pair A=(0,0), B=(3,0), C=(-6,0); draw(Circle(A,9)); draw(Circle(B,3)); draw(Circle(C,6)); [/asy]$

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
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1995 AIME Problems/Problem 4

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