6

6. [Maximum mark: 6]

The following diagram shows a circle with centre O and radius $r$ cm. Points A and B lie on the circle and $A\hat O B = \theta$ radians. Sector OAB is divided into two regions, a shaded segment P and a triangle Q. (Diagram shows a circle with sector OAB, segment P is the circular segment, triangle Q is $\triangle OAB$).

The area of the shaded segment P is 12.8 cm$^2$.
The areas of P and Q are in the ratio 3:5.
Find the value of $r$.