What is the area between the two circles?

**Natasha1** · May 8th 2006, 01:13 PM

If the length of AB is 20cm.

What is the area between the two circles?

**CaptainBlack** · May 8th 2006, 07:01 PM

Originally Posted by Natasha1

If the length of AB is 20cm.

What is the area between the two circles?

Label the centre of the circle $O$ , the midpoint of $AB$ $M$
the radius of the smaller circle $r_1$ and the radius of the outer circle $r_2$ .

Then triangle $OMB$ is a right triangle with hypotenuse $r_2$
and the other sides $r_1$ , and $10$ . Therefore by Pythagoras:

$ r_2^2=10^2+r_1^2 $ ,

or:

$ r_2^2-r_1^2=100 $

The area of the annulus is:

$ \pi r_2^2 - \pi r_1^2=\pi (r_2^2-r_1^2)=\pi.100 $

RonL

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