# 100 Days Streak problem!

Geometry Level 4

Consider $$\Delta ABC$$ such that $$AB=AC=10$$. Plot $$100$$ distinct points on the side $$BC$$.Define $$a_i =AP_i^2+P_iB . P_iC$$ , then find the value of

$\Large \sum_{i=1}^{100} a_i$

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