Online Geometry Problems

Infographic Geometry Problem 1059: Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Reflection of a Point over a Line, Collinear Points, Simson Line, Congruence. Level: High School, SAT Prep, College, Mathematics Education

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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.
 

Infographic Geometry problem: Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Reflection of a Point over a Line, Collinear Points, Simson Line, Congruence
 

 



 

 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 1051-1060 | Triangle | Circumcircle | Altitude | Orthocenter | Perpendicular lines | Circle | Reflection | Congruence | Simson line | Collinear Points | Email | Solution / comment | by Antonio Gutierrez
Last updated: Nov 12, 2014