theorem Th71: :: EUCLID13:88

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