100 Days Streak problem!

Geometry Level 4

Consider \(\Delta ABC\) such that \(AB=AC=10\). Plot \(100\) distinct points on the side \(BC\).Define \(a_i =AP_i^2+P_iB . P_iC\) , then find the value of

\[\Large \sum_{i=1}^{100} a_i\]

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