theorem Th70: :: EUCLID13:87

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