12. Let N, SE S2 be two opposite points and let Q be the tangent plane to S2 at N. Let H be the hemisphere of S2 closest to Q, and let f: H Q be the central projection. Suppose A, B E H\{N} be two distinct points. (a) Prove that if de(f(A), N) = de:(f(B),N) then dsz(A, S) = d(BS). (b) Prove that Zf(A)Nf(B) (as measured in Q) is the same as ZASB (as measured in S2)