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
![Click to view code [Asy_image]](http://alt2.artofproblemsolving.com/Forum/latexrender/pictures/d/e/a/dea9eb0c01eae787a68f8a35db84f31d797a88d7.png)
Note that
since
is the center of the larger circle of radius
. Using the Pythagorean Theorem on
,
Now using the Pythagorean Theorem on
,
Substituting
,
See Also
| 2004 AMC 12A (Problems) | ||
| Preceded by Problem 18 | Followed by Problem 20 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||





