2016 AIME I Problems/Problem 6
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Problem
In let
be the center of the inscribed circle, and let the bisector of
intersect
at
. The line through
and
intersects the circumscribed circle of
at the two points
and
. If
and
, then
, where
and
are relatively prime positive integers. Find
.
Solution
It is well known that and so we have
. Then
and so
and from the angle bisector theorem
so
and our answer is