100 Days Streak problem!

Geometry Level 4

Consider ΔABC\Delta ABC such that AB=AC=10AB=AC=10. Plot 100100 distinct points on the side BCBC.Define ai=APi2+PiB.PiCa_i =AP_i^2+P_iB . P_iC , then find the value of

i=1100ai\Large \sum_{i=1}^{100} a_i

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