Points and Squares

Geometry Level 3

Let \(ABC\) be a right-angled triangle at \(B\). Take points \(P_1, P_2, P_3, \dots , P_7\) on \(\overline {AC}\) such that \(AP_1 = P_1P_2 = \dots = P_6P_7 = P_7C\). If \(BP_1^2 + BP_2^2 + \dots + BP_7^2 = 70\), find the value of \(\overline{AC}\).

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