[math-fun] Fano Plane puzzle

Let F be the Fano Plane. Let FL be the set of 7 lines in F. Let FP be the set of 7 points in F. For L in FL, let P(L) be the set of 3 points on L. Now let SP be a set of 7 points in general position in R^3. Let m : FP ó SP be a bijection. For each line of L of F, let C(L) be the circle in R^3 through the 3 points m(P(L)). Let SL = C(FL). Let S = (SL, SP). S is then a model of the Fano Plane in R^3 with circles for Fano lines and points for Fano points. If we scale S so that the largest circle has radius 1, how large can we make the radius of the smallest circle of S by judicious choice of SP?