Question: NON EUCLIDEAN GEOMETRY Let and ' be circles on E 2 or H 2 with distinct centers C and C' and (positive) radii r and

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 "".)

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