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 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 $P=DA+DB+DC$ is minimum when point $D$ lie on Centroid how can i prove it
 November 4th, 2011, 02:28 AM #2 Senior Member     Joined: Feb 2010 Posts: 706 Thanks: 141 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 $Q=(DA)^2+(DB)^2+(DC)^2=$Minimum. Then Point $P$ 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: 20,810 Thanks: 2153 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: 20,810 Thanks: 2153 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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