Coordinate Geometry: JEE Main 2022 Mathematics question

Consider three circles: ${C_1}:{x^2} + {y^2} = {r^2}$ ${C_2}:{(x - 1)^2} + {(y - 1)^2} = {r^2}$ ${C_3}:{(x - 2)^2} + {(y - 1)^2} = {r^2}$ If a line L : y = mx + c be a common tangent to C₁, C₂ and C₃ such that C₁ and C₃ lie on one side of line L while C₂ lies on other side, then the value of $20({r^2} + c)$ is equal to :