Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 844.

## Wednesday, January 2, 2013

### Problem 844: Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity

Labels:
centroid,
circumcenter,
median,
perpendicular,
similarity,
triangle

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In Problem 843, it is easy to show that

ReplyDeleteAPCG is a parallelogram.

So CP=AG=2/3×AD, GP=BG=2/3×BE.

By Problem 843,

HO3×CP=HO1×GP

⇒ HO3×2/3×AD=HO1×2/3×BE

⇒ HO3×AD=HO1×BE