theorem :: EUCLID12:67

for A, B, C being Point of (TOP-REAL 2) st A,B,C is_a_triangle holds

( 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).| )

( 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).| )