Awesome geometry - 2

Point P is in the interior of $\angle$ ABC,

BP = 10 , $\angle$ ABC = 30 $^\circ$ .

Circle with center P and radius 2 is reflected in rays BA and BC respectively to form circles with centers Q and R .

If $A(\triangle BQR)$ can be expressed as $A \sqrt{B}$ where $B$ is square-free.

Find $A + B$

Details and Assumptions :

$\bullet$ $A(\triangle BQR)$ denotes area of $\triangle BQR$ .

This problem is part of set Awesome ' NIHARIAN' geometry