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:
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!