Awesome geometry - 2

Geometry Level 5

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

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