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Topic: Equals areas => centroid (Read 518 times) |
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Aryabhatta
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Equals areas => centroid
« on: Jun 20th, 2007, 3:07pm » |
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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?
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| « Last Edit: Jun 20th, 2007, 5:31pm by Aryabhatta » |
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rmsgrey
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Re: Equals areas => centroid
« Reply #1 on: Jun 21st, 2007, 7:43am » |
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on Jun 20th, 2007, 3:07pm, 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? |
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The second question does rather give away the answer to the first:
1)If PABC is a square, then each of the three triangles is half the square. There are other counterexamples too.
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Aryabhatta
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Re: Equals areas => centroid
« Reply #2 on: Jun 21st, 2007, 10:10am » |
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Yes it does, but could have been a trick question 
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