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Infographic Geometry Problem 1058: Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle, Circle, Diameter. Level: High School, SAT Prep, College, Mathematics Education

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In a triangle ABC, BH is the altitude and BD is a diameter of the circumcircle O (see the figure below). HE and HF are perpendicular to AB and BC at E and F, respectively. DE and DF meet AC at G and M, respectively. If S1 = area of triangle AEG, S2= area of triangle CFM, and S3 = area of triangle DGM, prove that S1 + S2 = S3.
 

Infographic Geometry problem: Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle, Circle, Diameter
 

 



 

 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 1051-1060 | Triangle | Area | Triangle Area | Altitude | Perpendicular lines | Circle | Circumcircle | Diameter | Email | by Antonio Gutierrez

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Last updated: Dec 2, 2014