Concentric Circles and a Chord (Posted on 2023-07-19)

	Submitted by Brian Smith
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For clarity, call the radius of the large circle x and the radius of the small circle y. Then the area we want can be written as pi*(x^2-y^2) Draw the diameter containing point C. Let E be the endpoint closer to C and F be the further endpoint. Then EC=x-y and CF=x+y. Now AB and EF are intersecting chords at point C. Then AC*CB=EC*CF; which simplifies to AC*CB = x^2-y^2. Then the area we want to compute is AC*CB*pi. With the dimensions given there are two possible orders for points A, B, C, and D. As suggested by the problem text one order is A, C, D, B. Then AC=7 and CB=CD+DB=13 which make a final area of 91pi. But as Jer noted, the problem still makes sense when C and D are flipped for an order of A, D, C, B. Then AC=7 and CD=DB-CD=1 which makes a final area of 7pi.

	Subject	Author	Date
	Subj	Rudyard Nolan	2023-09-04 10:42:59
	Puzzle Answer	K Sengupta	2023-08-26 23:13:49
	Math	Joshua Cobbs	2023-08-26 13:35:43
	Boost Your Luck: Insider Tips For Success In Online Matka On Matkabull	matkabull	2023-07-21 00:39:47
	Both solutions	Jer	2023-07-19 08:57:10
	Solution	Larry	2023-07-19 08:22:25
	solution	Charlie	2023-07-19 08:19:47