Possible length of a segment
Source: 43rd International Tournament of Towns, Junior A-Level P3, Fall 2021
February 18, 2023
geometrylengthsTournament of Towns
Problem Statement
The hypotenuse of a right triangle has length 1. Consider the line passing through the points of tangency of the incircle with the legs of the triangle. The circumcircle of the triangle cuts out a segment of this line. What is the possible length of this segment?Maxim Volchkevich