Equilateral Triangle with a Point

Given an equilateral triangle $ABC$ , and a point inside $ABC$ as $P$ . Given, $PA=a, PB=b, PC=c$ and $AB=l$ . We have $l=\sqrt{\dfrac{a^2+b^2+c^2}p+q\sqrt{r}D} ,$ where $D$ is the area of the triangle formed by $PA,PB$ and $PC$ .

It is given that $p,q$ and $r$ are positive integers with $r$ square-free. Find $pqr$ .