RPS #010 - Celebrating 500 Problems Solved

Geometry Level 3

In triangle A B C ABC , let A D AD , B E BE and C F CF be its medians, and Z Z as its centroid. If [ A B C ] [ABC] defines the area of triangle A B C ABC , find the value of [ A B Z ] + [ B C Z ] + [ C A Z ] [ D E F ] \frac{[ABZ] + [BCZ] + [CAZ]}{[DEF]}


The answer is 4.

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Rimba Erlangga by Rimba Erlangga , 23, Indonesia

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1 solution

For the time being I'll just leave with a descriptive solution .

WLOG you can assume the triangle to be an equilateral one . It'll be much easier that way. I'll post a full solution after some time, gotta go .

And Congratulations on solving 500 questions, I hope that you'll soon post a question with the title "Celebrating 1000 Problems solved " .

1 Helpful 0 Interesting 0 Brilliant 1 Confused

But there is a way to solve in general without assuming the triangle is equilateral

Thanks for your participation (y)

Rimba Erlangga - 6 years, 4 months ago

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