Area Common to 2 Circles: Radians Question

[david18]

"two circles of radii 5cm and 12cm are drawn, partly overlapping. Their centres are 13cm apart. Find the area common to the 2 circles"

I'm not quite sure how to do this. I think I am meant to be using the area of sector as if I draw a line down the middle of the area formed I can use the 1/2r^2(x-sinx) but I don't know how I can find the angle of the triangle that is formed.

Any help?

 

[Tedjn]

Try drawing a triangle connecting a point of intersection of the two circles and the two centers of the two circles. Technically, you can then find the angle formed by the line connecting the two centers with one of the other sides of the triangle using the law of cosines, but because the side lengths of the resulting triangle are 5-12-13, it is much easier to find sin x.

 

[physixguru]

Partly overlapping is INTERSECTING.