
theorem
  for A,B,C being Point of TOP-REAL 2 st A,B,C is_a_triangle holds
  the_diameter_of_the_circumcircle(A,B,C) = - |.C-A.|/ sin(angle (A,B,C))
  proof
    let A,B,C be Point of TOP-REAL 2;
    assume A,B,C is_a_triangle; then
    the_diameter_of_the_circumcircle(A,B,C) = |.C-A.|/ sin angle (C,B,A)
    by Thm29
    .= |.C-A.| / (- sin angle(A,B,C)) by EUCLID_6:2
    .= - |.C-A.| / sin angle(A,B,C) by XCMPLX_1:188;
    hence thesis;
  end;
