reserve n for Nat,
        lambda,lambda2,mu,mu2 for Real,
        x1,x2 for Element of REAL n,
        An,Bn,Cn for Point of TOP-REAL n,
        a for Real;
 reserve Pn,PAn,PBn for Element of REAL n,
         Ln for Element of line_of_REAL n;
reserve A,B,C for Point of TOP-REAL 2;
reserve x,y,z,y1,y2 for Element of REAL 2;
reserve L,L1,L2,L3,L4 for Element of line_of_REAL 2;
reserve D,E,F for Point of TOP-REAL 2;
reserve b,c,d,r,s for Real;

theorem
  A,B,C is_a_triangle implies
  the_radius_of_the_circumcircle(A,B,C) = |.the_circumcenter(A,B,C)-B.| &
  the_radius_of_the_circumcircle(A,B,C) = |.the_circumcenter(A,B,C)-C.|
  proof
    assume
A1: A,B,C is_a_triangle;
    then |.the_circumcenter(A,B,C)-A.| = |.the_circumcenter(A,B,C)-B.| &
    |.the_circumcenter(A,B,C)-A.| = |.the_circumcenter(A,B,C)-C.| by Th50;
    hence thesis by A1,Def4;
  end;
