2017 AMC 12B Problems/Problem 9
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Problem 9
A circle has center and has radius . Another circle has center and radius . The line passing through the two points of intersection of the two circles has equation . What is ?
Solution
The equations of the two circles are and . Rearrange them to and , respectively. Their intersection points are where these two equations gain equality. The two points lie on the line with the equation . We can simplify this like follows. \rightarrow \rightarrow \rightarrow \rightarrow . Thus,
See Also
2017 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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