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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 point, then prove that `OA+OB+OC=OD+OE+OF`

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To prove that \( OA + OB + OC = OD + OE + OF \) where \( D, E, F \) are the midpoints of sides \( BC, CA, AB \) respectively of triangle \( ABC \) and \( O \) is any point, we can follow these steps: ### Step 1: Define the midpoints Let \( D, E, F \) be the midpoints of sides \( BC, CA, AB \) respectively. By the definition of midpoints, we have: \[ D = \frac{B + C}{2}, \quad E = \frac{C + A}{2}, \quad F = \frac{A + B}{2} \] ...
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