Remember this problem? The one where you had to find the area between two circles by only knowing the length of the tangent "chord" (the red line)?

That problem is solved using some (moderately) tricky geometry. But if you know that the problem is solvable, it's actually pretty easy to solve by simply using the formula for the area of the circle and a bit of logic.

Can you do it?

Answer: A=25pi

Inner circle: x1^2 + y1^2 = r1^2
Outer Circle: x2^2 + y1^2 = r2^2
Area to find: pi(r2^2) - pi(r1^2)
d=10 inches

pick a (x2,y2) to begin. Let's use y2 as d/2 = 5, so y2=5. For x2, we can use the radius of the inner circle, so x2=r1.

Now that we have common variables: let's plug them into the equations again:

1) x1^2 + y1^2 = r1^2
2) r1^2 + 5^2 = r2^2
3) A=pi(r1^2 +25) - pi(r1^2)

A=pi(r1^2) + 25pi - pi(r1^2)
--> pi(r1^2) cancels...

A = 25pi

Posted by dknite on 2002-05-10 07:27:02