Online Geometry Problems

Online Geometry Problem 780: Acute Triangle, Sum of Inradius and Circumradius, Distances from the Orthocenter to the Vertices. Level: High School, College, Mathematics Education

The figure below shows an acute triangle ABC with the orthocenter H, the inradius r, and the circumradius R.
Prove that HA + HB + HC = 2.(R + r).

Triangle, Sum of Inradius and Circumradius, Distances from the Orthocenter to the Vertices
 

 

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