KöMaL 2020 B5104

Let $A_1$, $B_1$ and $C_1$ denote the points of tangency of the incircle of triangle $ABC$ on the sides, and let $R$ and $r$ be the radii of the circumscribed and inscribed circles, respectively. Prove that the ratio of the areas of triangles $A_1B_1C_1$ and $ABC$ is $r:2R$.