theorem Thm34: :: EUCLID10:50

for A, B, C being Point of (TOP-REAL 2) st A,B,C is_a_triangle holds
( |.(A - B).| = (the_diameter_of_the_circumcircle (A,B,C)) * (sin (angle (A,C,B))) & |.(B - C).| = (the_diameter_of_the_circumcircle (A,B,C)) * (sin (angle (B,A,C))) & |.(C - A).| = (the_diameter_of_the_circumcircle (A,B,C)) * (sin (angle (C,B,A))) )