5.2.4.24 Various Problems on the Plane

In the angle \ (60^{\ circ} \) with the vertex \ (O \) the circle of the radius \ (2 \ sqrt {3} \) related to the sides of the angle at points \ (a \) and \ (b \). At the continuation of the segment \ (o \) for the point \ (a \) the point \ (p \) is taken so that \ (a p = 2 \). Through the point \ (p \) a straight circle crosses at points \ (m \) and \ (n \), and a beam \ (b \) - at point \ (q \), and \ (\ quad p m = n q \). Find the area of the triangle \ (O P Q \) if it is known that it does not exceed 27.