Isosceles Triangle

$\triangle{ABC}$ 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.