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Geometry Problem 1161: Scalene Triangle, 60 Degrees, Angle, Orthocenter, Circumcenter, Equilateral Triangle, Congruence. Level: School, College, Mathematics Education

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The figure below shows a triangle ABC (AB > BC) with orthocenter H and circumcenter O such that angle ABC = 60 degrees. Line OH extended intersects AB and BC at D and E, respectively. Prove that (1) BO = BH, (2) triangle BDE is equilateral, (3) DO = HE, (4) BD = AD + CE, (5) OH = AB - BC = AD - CE.

 

Geometry Problem 1161 Scalene Triangle, 60 Degrees, Angle, Orthocenter, Circumcenter, Equilateral Triangle, Congruence

 


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