NON EUCLIDEAN GEOMETRY

• Let and ' be circles on E² or H² with distinct centers C and C' and (positive) radii r and r', respectively.
• Consider the following three inequalities:(i) mCC' r + r', (ii) r mCC' + r', and (iii) r' mCC' + r.
• Prove the following claim:
• If and ' intersect in at least one point, then all three inequalities are true. Moreover, if they intersect in two points, then all three inequalities are strictly true. (They hold with "<" instead of "".)