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November 3rd, 2011, 07:36 PM   #1
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minimum value



In a given triangle we have to prove the value of

is minimum when point lie on Centroid

how can i prove it
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November 4th, 2011, 02:28 AM   #2
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Re: minimum value

Assuming all angles are less than 120 degrees ... you will have a tough time proving this. In general it is not true. Try Googling "Fermat Point".
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November 5th, 2011, 06:35 AM   #3
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Re: minimum value

thanks mrtwhs

Now if Minimum. Then Point is at Centroid or not

If Yes How can I prove it

thanks
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November 5th, 2011, 08:13 AM   #4
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Use coordinate geometry.
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November 6th, 2011, 02:25 AM   #5
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Re: minimum value

I want more light on that Method (Coordinate geometry)

thanks
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November 6th, 2011, 01:52 PM   #6
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Assign Cartesian coordinates for A, B, C and D, then express Q in terms of them and use "completing the square" to determine the coordinates for D that minimize Q.
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