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D, E, F are the midpoints of the sides b...

`D, E, F` are the midpoints of the sides `bar(BC), bar(CA) and bar(AB)` respectively of the triangle `ABC`. If P is any point in the planeof the triangle, show that `vec(PA) + vec(PB) +vec(PC) = vec(PD) + vec(PE) +vec(PF)`.

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