theorem Th49: :: EUCLID12:64

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 & A in circle (a,b,r) & B in circle (a,b,r) & C in circle (a,b,r) holds
( |[a,b]| = the_circumcenter (A,B,C) & r = |.((the_circumcenter (A,B,C)) - A).| )