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# Rolling a circle within a circle

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Posted 06 July 2013 - 09:44 PM

We have two circles.  One circle has a diameter of 12 cm's while another is D cm's.  The circle with the diameter of 12 cm's fits inside the other circle.  If rolled within the larger circle, the smaller circle rotates three times before coming back to rest at the same starting point.  That is, Point p in the smaller circle starts and stop at Point P' on the larger circle after three revolutions.

What is the diameter of the bigger circle?

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### #2 Nins_Leprechaun

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Posted 06 July 2013 - 10:49 PM

Spoiler for

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### #3 James33

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Posted 06 July 2013 - 11:42 PM

Just visualising it, won't there be multiple valid answers?

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Posted 06 July 2013 - 11:51 PM

Just visualising it, won't there be multiple valid answers?

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### #5 bonanova

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Posted 07 July 2013 - 07:48 AM

Spoiler for I think

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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### #6 Panther

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Posted 07 July 2013 - 10:47 AM

Spoiler for Pretty sure

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Posted 08 July 2013 - 03:50 AM

be careful with your analysis.  In this image we have a large circle and two smaller congruent circles that have 1/3 the diameter of the larger circle.  When both circles travel around the larger circle, do they in fact travel the same distance?

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### #8 bonanova

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Posted 08 July 2013 - 05:25 AM   Best Answer

Spoiler for

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #9 gavinksong

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Posted 09 July 2013 - 12:20 PM

Spoiler for

Wait, what?

Spoiler for I don't think that's right

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Posted 09 July 2013 - 12:41 PM

Spoiler for

Wait, what?

Spoiler for I don't think that's right

How big must the bigger circle be to do that?
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