In a triangle ABC,
H is the orthocenter and D is a point on the circumcircle O. D1,
D2, and D3 are the reflections of D over BC, AC,
and AB, respectively. DH meets the Simson line for D at F. Prove that
D1, H, and D3 are collinear points; (2) D2D3
= 2.SM; (3) F is the midpoint of DH.