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Subject: "area between 3 circles"     Previous Topic | Next Topic
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tiusic
Member since Nov-10-06
Nov-10-06, 09:25 PM (EST)
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"area between 3 circles"
 
   I came across this very interesting puzzle earlier today and after a little work, I think I have the answer (but it was an open question with no given answer so i can't check).
Find the formula for the shaded area in the picture below from the circles' radii of a, b, c.


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tiusic
Member since Nov-10-06
Nov-12-06, 01:28 AM (EST)
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1. "RE: area between 3 circles"
In response to message #0
 
   I managed to check my answer with Geometer's Sketchpad and it's correct. Anyone else got an answer?


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alexbadmin
Charter Member
1915 posts
Nov-13-06, 03:08 AM (EST)
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2. "RE: area between 3 circles"
In response to message #1
 
   There is a straightforward solution using Heron's formula for a triangle with sides (a+b), (b+c) and (a+c), from which sectors of each circle are subtracted. The central angles can be found from the Law of Cosines in that triangle.


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