# What is the area between the two circles?

• May 8th 2006, 01:13 PM
Natasha1
What is the area between the two circles?
If the length of AB is 20cm.

What is the area between the two circles?
• May 8th 2006, 07:01 PM
CaptainBlack
Quote:

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