They are hundred in number

$\Delta ABC$ is an isosceles triangle with $AB=AC=2$ . There are $100$ points $P_1,P_2,P_3,\ldots, .P_{100}$ on the side $BC$ .

Write

$\large{m_i = AP_i^2 + BP_i . P_iC \qquad { (i=1,2,3,\ldots,100)}}$

Find the value of $m_1+m_2+\cdots +m_{100}$ .