All dashed lines are Inversion with respect to the red circle with radius R. Point O is the Inversion Center. Radius of larger Green Circle = r_1 Radius of Inversed Larger Green Circle = R OB × OB′ = R^2 OB × (R + 2R) = R^2 OB = (R^2 /(3R)) = (R/3) r_1 = ((R − (R/3))/2) = (R/3) Radius of Larger Pink Circle = r_2 Radius of Inversed Larger Pink Circle = a (R + a)^2 = (R − a)^2 + R^2 2aR = −2aR + R^2 ⇒ a = (R/4) OC × OC′ = R^2 OC × (R + 2((R/4))) = R^2 OC = (R^2 /((3R)/2)) = ((2R)/3) r_2 = ((R − ((2R)/3))/2) = (R/6)