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
(1) D2,
D1, H, and D3 are collinear points; (2) D2D3
= 2.SM; (3) F is the midpoint of DH.
![Geometry Problem 1059 Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Reflection of a Point over a Line, Collinear Points, Simson Line, Congruence Infographic Geometry problem: Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Reflection of a Point over a Line, Collinear Points, Simson Line, Congruence](p1059-triangle-circle-simson-line-reflection-parallel-perpendicular-math.gif)
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