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        riddles >> medium >> Equals areas => centroid
        
(Message started by: Aryabhatta on Jun 20th, 2007, 3:07pm)
Title: Equals areas => centroid
Post by Aryabhatta on Jun 20th, 2007, 3:07pm
In a 2D plane, you are given a triangle ABC and a point P such that the areas of the triangles PAB, PBC and PCA are equal.

1) Prove/Disprove: P must be the centroid of the triangle ABC.

2) What if the point P was required to be within the triangle ABC?
Title: Re: Equals areas => centroid
Post by rmsgrey on Jun 21st, 2007, 7:43am

on 06/20/07 at 15:07:07, Aryabhatta wrote:
In a 2D plane, you are given a triangle ABC and a point P such that the areas of the triangles PAB, PBC and PCA are equal.

1) Prove/Disprove: P must be the centroid of the triangle ABC.

2) What if the point P was required to be within the triangle ABC?


The second question does rather give away the answer to the first:

1)[hide]If PABC is a square, then each of the three triangles is half the square. There are other counterexamples too.[/hide]
Title: Re: Equals areas => centroid
Post by Aryabhatta on Jun 21st, 2007, 10:10am
Yes it does, but could have been a trick question  :P


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