Question 30$ABC$ is an isosceles triangle with $AB=AC=3$. There are $k$ distinct points on $BC$, denoted by $P_1,P_2,\ldots,P_k$. Let $x_i=AP_i^2+BP_i\cdot P_iC$ where $i=1,2,\ldots,k$. Find the value of $k$ if $x_1+x_2+\cdots+x_k=1080$.