Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 14"
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Revision as of 15:50, 3 April 2012
Problem
Three points ,
, and
are fixed such that
lies on segment
, closer to point
. Let
and
where
and
are positive integers. Construct circle
with a variable radius that is tangent to
at
. Let
be the point such that circle
is the incircle of
. Construct
as the midpoint of
. Let
denote the maximum value
for fixed
and
where
. If
is an integer, find the sum of all possible values of
.
Solution
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