show that the medians of a triangle ABC are coincident

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- May 13th 2009, 03:01 PMReignrxneed help prove Medians of a triangle coincident
show that the medians of a triangle ABC are coincident

- May 13th 2009, 04:37 PMPlato
- May 13th 2009, 05:00 PMKrizalid
- May 13th 2009, 05:58 PMReignrx
thanks

- May 14th 2009, 09:34 AMpankaj
Let , denote the vertices respectively and also assume denote the mid-points of respectively.Therefore,

Now, is the position vector of the point on median which divides in the ratio .Simlarly, is the position vector of the point on median which divides in the ratio and is the position vector of the point on median which divides in the ratio .

Since these position vectors have turned out to be equal,obviously are concurrent and the point of concurrency is