2002 AIME II Problems/Problem 15

Problem

Circles $\mathcal{C}_{1}$ and $\mathcal{C}_{2}$ intersect at two points, one of which is $(9,6)$ , and the product of the radii is $68$ . The x-axis and the line $y = mx$ , where $m > 0$ , are tangent to both circles. It is given that $m$ can be written in the form $a\sqrt {b}/c$ , where $a$ , $b$ , and $c$ are positive integers, $b$ is not divisible by the square of any prime, and $a$ and $c$ are relatively prime. Find $a + b + c$ .

Solution

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2002 AIME II (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Last Question
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2002 AIME II Problems/Problem 15

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