2006 AMC 12A Problems/Problem 16
Problem
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Circles with centers and
have radii
and
, respectively. A common internal tangent intersects the circles at
and
, respectively. Lines
and
intersect at
, and
. What is
?
Solution
and
(vertical angles) are congruent, as are right angles
and
(since radii intersect tangents at right angles). Thus,
.
By the Pythagorean Theorem, line segment . The sides are proportional, so
. This makes
and
.
See also
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Preceded by Problem 15 |
AMC 12A 2006 |
Followed by Problem 17 |
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