theorem :: EUCLID10:39

for A, B, C being Point of (TOP-REAL 2)
for a, b, r being Real st A,B,C is_a_triangle & angle (C,B,A) in ].0,PI.[ & angle (B,A,C) in ].0,PI.[ & A in circle (a,b,r) & B in circle (a,b,r) & C in circle (a,b,r) & |[a,b]| in LSeg (A,C) holds
angle (C,B,A) = PI / 2