For any X and Y of subsets of R² we define "distance H" between X and Y by the expression: dH (X, Y ) = inf { > 0 : X Y e Y X}

where inf is an infimum and X is the union of euclidian discsof radius , centered in X: X = xX {p R² : dE (p, x) }, where dE is the ordinary euclidean distance.

Calculate

i) dH (C1, C2) where C1, C2 are two circles of R² with respective radiuses r e R, r > R, that has only one point in common. (touch each other only in one point) ii) dH (P, S) where P is is a dot and S is a circle with radius R and center C. iii) dH (l1, l2) where l1, l2 are two Euclidian paralel iv) dH (l1, l2) where l1, l2 are two Euclidian lines that touch each other only in one dot