SMO 2009 Open Round 1 Question 3

Let $P_1,P_2,\ldots,P_{41}$ be $41$ distinct points on the segment $BC$ of triangle $ABC$, where $AB=AC=7$. Evaluate $\displaystyle\sum_{i=1}^{41}(AP_i^2+P_iB\cdot P_iC)$.