Mock AIME II 2012 Problems/Problem 8
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Problem
Let be a point outside circle
with center
and radius
such that the tangents from
to
,
and
, form
. Let
first intersect the circle at
, and extend the parallel to
from
to meet the circle at
. The length
, where
,
, and
are positive integers and
is not divisible by the square of any prime. Find
.
Solution
Let intersect
at
.
Note that
, thus
. Then we have
. We can use the law of cosines to find
,
.
Thus, we have
.