# They are hundred in number

Geometry Level pending

$$\Delta ABC$$ 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 $$m_1+m_2+\cdots +m_{100}$$.

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