2006 AMC 12A Problems/Problem 19
Problem
Circles with centers and have radii and , respectively. The equation of a common external tangent to the circles can be written in the form with . What is ?
Solution
Let be the line that goes through and , and let be the line . If we let be the measure of the acute angle formed by and the x-axis, then . clearly bisects the angle formed by and the x-axis, so . We also know that and intersect at a point on the x-axis. The equation of is , so the coordinate of this point is . Hence the equation of is , so , and our answer choice is .
See also
2006 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 18 |
Followed by Problem 20 |
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All AMC 12 Problems and Solutions |
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