IZhO 2021 Problem 4

Let there be an incircle of triangle $ABC$ , and 3 circles each inscribed between incircle and angles of $ABC$ . Let $r, r_1, r_2, r_3$ be radii of these circles ( $r_1, r_2, r_3 < r$ ). Prove that $$r_1+r_2+r_3 \geq r$$