Mock AIME 1 2006-2007 Problems/Problem 14
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 .
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