
theorem Thm31:
  for A,B,C be Point of TOP-REAL 2 st A,B,C is_a_triangle holds
  the_diameter_of_the_circumcircle(A,B,C)=
  - the_diameter_of_the_circumcircle(B,A,C)
  proof
    let A,B,C be Point of TOP-REAL 2;
A3: |.B-A.|=|.A-B.| & |.A-C.|=|.C-A.| & |.C-B.|=|.B-C.| by EUCLID_6:43;
    the_diameter_of_the_circumcircle(B,A,C)=
     |.A-B.|*|.C-A.|*|.B-C.|/2/( - the_area_of_polygon3(A,B,C)) by A3,Thm28
    .= - |.A-B.|*|.C-A.|*|.B-C.|/2/the_area_of_polygon3(A,B,C)
    by XCMPLX_1:188;
    hence thesis;
  end;
