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 = 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:

area =

b. Show that the area of the shaded segment is

This is where I get stuck.

I can find the area of the sector OBC using the formula and get

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

Having said that, multiplying out gives:

, so the area of the triangle must be .

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