Question

In the diagram, OPQ is a sector of a circle, centre O and radius r cm. Angle QOP = Theta radians. The tangent to the circle at Q meets OP extended at R.

(i) Show that area, A cm^2, of the shaded region is given by A=(r^2/2)(tan theta- theta).

(ii) In the case where theta=0.8 and r= 15, evaluate the length of the perimeter of the shaded region.