
theorem Thm32:
  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(A,C,B)
  proof
    let A,B,C be Point of TOP-REAL 2;
    assume A,B,C is_a_triangle; then
A2: A,C,B is_a_triangle & B,C,A is_a_triangle by MENELAUS:15;
    the_diameter_of_the_circumcircle(A,B,C)
    =the_diameter_of_the_circumcircle(B,C,A) by Thm27
    .= - the_diameter_of_the_circumcircle(C,B,A) by A2,Thm31;
    hence thesis by Thm27;
  end;
