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
See Also
2004 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 18 |
Followed by Problem 19 |
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All AMC 12 Problems and Solutions |