In fact, the simplest case (n=2) follows from Stewart's theorem (see Stewart.html ).

Setting B=A

(k

The previous equality reduces also inductively the sum for a general n. In this case replace simply the two first terms k

(k

D is a point independent of the value of k and the given equation:

k

(k

The proposition follows by repeatedly applying the previous step.

Stewart.html

WeightedSumsOfDistances.html

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