theorem :: EUCLID13:81

for A, B, C being Point of (TOP-REAL 2) st A,B,C is_a_triangle & |((B - A),(B - C))| <> 0 & not |.(A - B).| * (sin (angle (A,B,(the_foot_of_the_altitude (A,B,C))))) = |.((the_foot_of_the_altitude (A,B,C)) - A).| holds
|.(A - B).| * (- (sin (angle (A,B,(the_foot_of_the_altitude (A,B,C)))))) = |.((the_foot_of_the_altitude (A,B,C)) - A).|