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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