# It seems to the sum of squares

Geometry Level 4

$\large \sum_{k=1}^{n-1} \left(\overline{CP_k}\right)^2$

Let $$\triangle ABC$$ be a right triangle with $$\angle C = 90^\circ$$ and $$AB=c$$. If we divide side $$AB$$ into $$n$$ equal parts by points $$P_1, P_2, \ldots, P_{n-1},$$ what is the value of the above sum?

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