Difference between revisions of "2013 Mock AIME I Problems/Problem 1"
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* [[2013 Mock AIME I Problems/Problem 2|Followed by Problem 2]] | * [[2013 Mock AIME I Problems/Problem 2|Followed by Problem 2]] |
Latest revision as of 08:01, 30 July 2024
Problem 1
Two circles and , each of unit radius, have centers and such that . Let be the midpoint of and let be a circle externally tangent to both and . and have a common tangent that passes through . If this tangent is also a common tangent to and , find the radius of circle .
Solution
Let be the center of circle and be the point of tangency between and . Note that triangles and are similar, so and . Thus the radius of is .
See Also
- 2013 Mock AIME I Problems
- Preceded by
- Followed by Problem 2