All possible values of the length of a segment
Source: Paraguayan National Olympiad 2009, Level 3, Problem 5
August 31, 2014
Problem Statement
In a triangle , let be its incenter. The distance from to the segment is and the distance from that point to vertex is . Let be a point in the plane region between segments and such that is the center of a circumference that is tangent to lines and and passes through . Find all possible values of the length .