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if D,E and F are the mid-points of the s...

if D,E and F are the mid-points of the sides BC,CA and AB respectively of the `DeltaABC and O` be any points, then prove that `OA+OB+OC=OD+OE+OF`

Text Solution

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Since, D is the mid-point of Bc, therefore by section formula, we have

`OD=(OB+OC)/(2)`
`implies OB+OC=2OD` . . . (i)
Similarly, `OC+OA=2OE` . . (ii)
and `OB+OA=2OF` . . . (iii)
On adding Eqs. (i), (ii) and (iii), we get
`2(OA+OB+OC)=2(OD+OE+OF)`
`impliesOA+OB+OC=OD+OE+OF` Hence proved.
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