theorem Th67: :: EUCLID13:80

for A, B, C being Point of (TOP-REAL 2) st B <> C & the_foot_of_the_altitude (A,B,C),B,A is_a_triangle & 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).|