Mock AIME 1 2006-2007 Problems/Problem 14
Revision as of 15:50, 3 April 2012 by 1=2 (talk | contribs) (moved Mock AIME 1 2006-2007/Problem 14 to Mock AIME 1 2006-2007 Problems/Problem 14)
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
This problem needs a solution. If you have a solution for it, please help us out by adding it.