# Isosceles Triangle

**Geometry**Level 5

\(\triangle{ABC}\) is an isosceles triangle with \(AB=AC=2\) cm. There are \(100\) points \(P_1, P_2, \cdots, P_{100}\) on the side \(BC\). Find the value of \[\sum_{i=1}^{100}AP_i^2+BP_i \cdot P_iC.\]

**Details and assumptions**

The points need not be equally spaced.