theorem Th55: :: EUCLID12:74

for a being Real
for A, B, C being Point of (TOP-REAL 2)
for b, r being Real st A,B,C is_a_triangle & 0 < angle (C,B,A) & angle (C,B,A) < PI & A in circle (a,b,r) & B in circle (a,b,r) & C in circle (a,b,r) holds
the_diameter_of_the_circumcircle (A,B,C) = 2 * r