VTMO 2026 - Grade 10 - Semifinal - SET 1 - Self-study Question 1

A sequence of circles $(O_1;r_1),(O_2;r_2),(O_3;r_3),\ldots$ is tangent to both sides of angle $xOy$, with consecutive circles externally tangent as shown. Given $r_1=1$ and $r_2=2$, find $r_{2020}$.