Difference between revisions of "2004 AMC 12A Problems/Problem 19"
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Problem 19
Circles and are externally tangent to each other, and internally tangent to circle . Circles and are congruent. Circle has radius and passes through the center of . What is the radius of circle ?
Solution
Note that since D is the center of the larger circle of radius 2
Using the Pythagorean Theorem on
Now Using the pythagorean theorem on
Substituting in