#0, area between 3 circles
Posted by tiusic on Nov-10-06 at 09:25 PM
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.
http://web.gnowledge.org/wiki/images/6/61/Threecirclesareabetween.JPG
#1, RE: area between 3 circles
Posted by tiusic on Nov-12-06 at 01:28 AM
In response to message #0
I managed to check my answer with Geometer's Sketchpad and it's correct. Anyone else got an answer?
#2, RE: area between 3 circles
Posted by alexb on Nov-13-06 at 03:08 AM
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.
|