MathDB

4

Part of 2021 International Zhautykov Olympiad

Problems(1)

IZHO P4 (Day 2, Problem 1)

Source: IZHO 2021

1/9/2021
Let there be an incircle of triangle ABCABC, and 3 circles each inscribed between incircle and angles of ABCABC. Let r,r1,r2,r3r, r_1, r_2, r_3 be radii of these circles (r1,r2,r3<rr_1, r_2, r_3 < r). Prove that r1+r2+r3≥rr_1+r_2+r_3 \geq r
IZHO 2021izhogeometric inequalitygeometryinequalities