Circle

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 :