Sum of radii of incircle and excircles
Source: Kvant Magazine No. 10 2023 M2767
February 6, 2024
geometrylengthsincircle
Problem Statement
It is easy to prove that in a right triangle the sum of the radii of the incircle and three excircles is equal to the perimeter. Prove that the opposite statement is also true.Proposed by I. Weinstein