November 3rd, 2011, 07:36 PM  #1 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  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 
November 4th, 2011, 02:28 AM  #2 
Senior Member Joined: Feb 2010 Posts: 714 Thanks: 151  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".

November 5th, 2011, 06:35 AM  #3 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  Re: minimum value
thanks mrtwhs Now if Minimum. Then Point is at Centroid or not If Yes How can I prove it thanks 
November 5th, 2011, 08:13 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,018 Thanks: 2251 
Use coordinate geometry.

November 6th, 2011, 02:25 AM  #5 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  Re: minimum value
I want more light on that Method (Coordinate geometry) thanks 
November 6th, 2011, 01:52 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,018 Thanks: 2251 
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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