# 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.

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