for A, B, C being Point of (TOP-REAL 2) st A,C,B is_a_triangle & angle (A,C,B) < PI holds
( angle (B,A,C) = ((arctan ((cot ((angle (A,C,B)) / 2)) * ((|.(C - B).| - |.(C - A).|) / (|.(C - B).| + |.(C - A).|)))) + (PI / 2)) - ((angle (A,C,B)) / 2) & angle (C,B,A) = ((PI / 2) - ((angle (A,C,B)) / 2)) - (arctan ((cot ((angle (A,C,B)) / 2)) * ((|.(C - B).| - |.(C - A).|) / (|.(C - B).| + |.(C - A).|)))) )