Tricky Area (Posted on 2002-05-10)

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?

	Submitted by levik
Rating: 3.5714 (7 votes)
Solution:	(Hide)
The problem asks us to determine the area between the circles by simply knowing the length of the longest chord. The fact that it's solvable, means that the radii of the two circles are not important, and as long as the chord stays the same length, the solution won't change. Imagine then, a scenario where the inner circle's radius is zero. The area should still be the same since changing the radius shouldn't matter. But then the 10 inch chord becomes the diameter of the large circle. Since the inner circle's area is zero, the area between the circles is equal to the area of the bigger one: A = (pi)R^2 = (pi)(10/2)^2 = 25(pi)

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2024-03-08 08:58:01
	solution belated	salil	2006-02-25 07:13:42
	Solution: Independent of the radii	Shiv	2004-10-12 05:10:24
	Why 10 inches?	Vinodhan Selvarajalu	2003-05-08 01:04:09
	re: Tricky	Ravi Raja	2003-03-03 17:50:14
	I had already posted its solution	Ravi Raja	2003-03-03 17:43:34
	solution	Justin	2002-05-11 05:08:05
	comment to dknite	TomM	2002-05-10 18:26:10
	solution via circle equation	dknite	2002-05-10 07:27:02
	Elegant	TomM	2002-05-10 07:24:18
	Tricky	Happy	2002-05-10 06:11:59