Consider the picture to the right. We have two concentric circles, one inside another. We do not know the radius for either one of them.

We do, however know that the chord (shown in red) - a line whose ends are on the outer circle and which is tangent to the inner circle - has a length of 10 inches.

What is the area (shaded in light-blue) between the two circles?

Make a rectangular triangle of sides 5, R1 and an hypotenusa of R2. Using Pitagoras theorem we get 25=R2²-R1²
The area between the two circles is Pi*R2²-Pi*R1²=Pi*(R2²-R1²). So we simply put 25 instead of R2²-R1² and the result is:
Area=25*Pi=78.5398163398 in²

Posted by Antonio on 2003-08-22 05:31:02