# Thread: Circular square

1. ## Circular square

The picture says it all.

2. ## Re: Circular square

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Exactly half (50%)</span hide>

3. ## Re: Circular square

Correct

I have found with this puzzle some people take one look at it and give the answer straight away, others get out the calculators.

4. ## Re: Circular square

It did take Hans 9 minutes ... assuming that he open your post the minute you made it

5. ## Re: Circular square

No, I didn't see the post immediately.

The idea is: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">side of the large square = diameter of circle = diagonal of small square = side of small square * square root of 2, so area of large square = area of small square * (square root of 2)^2 = area of small square * 2</span hide>

6. ## Re: Circular square

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">If the inside square is rotated by 45

7. ## Re: Circular square

Yep, then it's trivial.

8. ## Re: Circular square

Not quite so trivial this time. Same problem, but with equilateral triangles. And your time starts... NOW!

Alan

<small>Hints for Tony - all you need to know to solve this problem is that a triangle has three sides and a circle is round. HTH <img src=/S/sarcasm.gif border=0 alt=sarcasm width=15 height=15> <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

9. ## Re: Circular square

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1/4</span hide>

10. ## Re: Circular square

Correct (of course). And I won't take the "time taken" into consideration when awarding the final mark. <img src=/S/grin.gif border=0 alt=grin width=15 height=15>
<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">This is another one where rotation of the inner triangle (by 180

11. ## Re: Circular square

Actually, I took more time than necessary. I initially overlooked the word "equilateral", so I started looking for a general solution. I soon came to the conclusion that the proportion wasn't constant, so I took another look at the question. Then I noticed the "equilateral". <img src=/S/doh.gif border=0 alt=doh width=15 height=15>

12. ## Re: Circular square

... and for us that see things differently, I would have said none as the small square is covering the circle as I see it, not the large square. Perhaps this is why I never try to figure out these puzzles. <img src=/S/dizzy.gif border=0 alt=dizzy width=15 height=15>

13. ## Re: Circular square

OK, let's raise the ante.
How about the area ratios of n-sided regular polygons that inscribe and circumscribe the circle?

Alan

The clock is running...

14. ## Re: Circular square

I was out and only saw your new puzzle 40 minutes after you posted it.

The ratio is cos

15. ## Re: Circular square

Pretty good then - 11 minutes give or take. Or just over a minute per polygon sounds even better! <img src=/S/bravo.gif border=0 alt=bravo width=16 height=30>

Alan

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