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Another Circle Puzzle

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Another puzzle I found on John Baez's blog. It seems to have been discovered and published only as recently as 2011. Baez's post gives a reference.

Two touching semi-circles, aligned as shown, are inscribed in a circle.

You might think you need more information, such as the relative sizes of the semi-circles perhaps. But in fact it doesn't make any difference.

I will post my solution on 6 March.

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SXR103 chemistry is fun (2008) :-)

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IF you maximise the red semicircle and minimise the blue semicircle, 

THEN you end up with a semicircle that has its straight side as the diameter of the outer circle. 

THEREFORE Therefore the total of the 2 semicircles covers half the area of the outer circle.

Jan (who has time now to catch up on blogs after submitting MST124 TMA03 6 days early smile)

Richard Walker

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That's true Jan but it only works given my statement that the relative sizes are irrelevant, i think you need to prove this fact before you can say the solution is complete 🙂

SXR103 chemistry is fun (2008) :-)

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Hi Richard,

I'm being lazy today.  I think I'll wait until I see your solution smile