Online Geometry theorems, problems, solutions, and related topics.
Geometry ProblemLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 842.
By Problem 841, HM=BE/2, HN=AD/2∴ HO4×HM=HO2×HN⇒ HO4×BE/2=HO2×AD/2⇒ HO4×BE=HO2×AD
From problem 841, HM=BE/2 ; HN=AD/2 and HO4*HM = HO2*HN It simply leads to the result HO4*BE = HO2*AD
Note that the result is true for any point G inside triangle ABC.Peter Tran