There is a question on the area of a sector of a circle on which I am stuck and was wondering whether anyone could give me a pointer.

I have attached an image of the diagram to which the question refers...

The diagram shows an arc of ABC of a circle centre o and radius 10cm.

Angle AOB = $\displaystyle \theta$ radians and angle AOC is a right angle.

a. Write down, in terms of theta, the area of sector AOB.

I can do this easily enough: $\displaystyle area = \frac{1}{2} r^2 * \theta$

area = $\displaystyle 50 \theta $

b. Show that the area of the shaded segment is $\displaystyle 25(\pi -2\theta - 2cos \theta)cm^2 $

This is where I get stuck.

I can find the area of the sector OBC using the formula and get $\displaystyle 50(\frac{\pi }{2} - \theta)$ = $ 25\pi - 50 \theta $

But I can't see how to get the area of the triangle.

Having said that, multiplying out $\displaystyle 25(\pi - 2\theta - 2 cos \theta)$ gives:

$\displaystyle 25\pi - 50\theta -50 cos\theta $, so the area of the triangle must be $\displaystyle 50 cos \theta $.

I just can't see how to get at this area for the triangle, though. Any advice would be greatly appreciated!