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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