theorem Th57:
  B <> A implies
  (sin angle(B,A,C) + sin angle(C,B,A)) * (|.C-B.| - |.C-A.|) =
  (sin angle(B,A,C) - sin angle(C,B,A)) * (|.C-B.| + |.C-A.|)
  proof
    assume B<>A;
    then |.C-B.| * sin angle(C,B,A) = |.C-A.| * sin angle(B,A,C) by EUCLID_6:6;
    hence thesis;
  end;
