They are hundred in number

Geometry Level 4

\(\Delta ABC\) 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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