2023 AMC 10A Problems/Problem 22
Circle and
each have radius
, and the distance between their centers is
. Circle
is the largest circle internally tangent to both
and
. Circle
is internally tangent to both
and
and externally tangent to
. What is the radius of
?
Solution
Connect the centers of and
, and the centers of
and
. Let the radius of
be
. Then, from the auxillary lines, we get
. Solving, we get
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