What Are Your Thoughts on This Simple Circle Problem?

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The discussion revolves around a geometric problem involving two circles and their radii. The user presents a diagram and outlines relationships between the segments, noting that OA is the radius of the larger circle and MA is the radius of the smaller circle. They apply the Pythagorean theorem to establish a connection between the lengths, suggesting that the equation combining OM and r equals R could be a solution. Participants are encouraged to explore these relationships further to solve the problem. The conversation emphasizes the importance of geometric principles in solving circle-related problems.
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Hi guys,

I found this little problem on some website ages go, and was just wondering what you think of it:

http://img354.imageshack.us/img354/9052/cirlce8hk.gif

Anyone have any ideas?
 
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|OA| = R (since OA is a radius of the big circle)
|OA| = |OM| + |MA| (just look at it)
|MA| = r (since AM is a radius of the small circle)
r² + r² = |OM|² (pythagorean theorem)
 
interesting, i was thinking that: Line OM + r = R

would that work?
 
That's what you get when you put AKG's first three lines together into a single equation. Now put that together with the fourth line, and you've got it
 

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