Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

Explanation

Let `O` is the center of regular octagon `ABCDEFGH`.

Please refer to video to see the regular octagon.

Now, `vec(OA) = -vec(OE)`

`vec(OB) = -vec(OF)`

`vec(OC) = -vec(OG)`

`vec(OD) = -vec(OH)`

Now, sum of all vectors drawn from the center of this octagon

`=vec(OA)+vec(OB)+vec(OC)+vec(OD)+vec(OE)+vec(OF)+vec(OG)+vec(OH)`

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