M2767

Part of Kvant 2023

Problems(1)

Sum of radii of incircle and excircles

Source: Kvant Magazine No. 10 2023 M2767

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

geometrylengthsincircle