# Quick geometry puzzle

Acolyte
Posers and Puzzles 03 Oct '03 15:55
1. Acolyte
Now With Added BA
03 Oct '03 15:55
Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?

(Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC ðŸ˜³)
2. richjohnson
TANSTAAFL
03 Oct '03 19:33
Originally posted by Acolyte
Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?

(Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC ðŸ˜³)
The way you've described it, the first circle would just touch the sides of the square, leaving no room for a second circle between it and the square. Perhaps you could rephrase your question?
3. 03 Oct '03 20:14
Originally posted by Acolyte
Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?

(Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC ðŸ˜³)

1:2
4. Acolyte
Now With Added BA
03 Oct '03 20:40
Originally posted by richjohnson
The way you've described it, the first circle would just touch the sides of the square, leaving no room for a second circle between it and the square. Perhaps you could rephrase your question?
Look at my avatar: the second circle has to fit in the grey area.
5. Acolyte
Now With Added BA
03 Oct '03 20:42
Originally posted by ivanhoe

1:2
Nope.
6. Phlabibit
Mystic Meg
03 Oct '03 22:14
Originally posted by Acolyte
Nope.
Just by eye I would say 1/16? I am at home, had I seen this at work I would have used my CAD to figure it out... as I have done with RC Math Quizes....

I will know some time this weekend if I am wrong.... and post the proper answer.

Phla-
7. royalchicken
CHAOS GHOST!!!
04 Oct '03 20:37
Originally posted by Acolyte
Look at my avatar: the second circle has to fit in the grey area.
I won't say anything answerwise, but this is a puzzle only a inscribed biscuiteer could invent ðŸ˜‰. I've had a good deal of trouble puzzling you too--else I'd post something in here.
8. Phlabibit
Mystic Meg
06 Oct '03 17:26
1 : 5.88

or

.17
9. 06 Oct '03 18:49
Originally posted by Phlabibit
1 : 5.88

or

.17
Thats almost, but not quite right. Not much more than pythagoras is needed I think...
10. royalchicken
CHAOS GHOST!!!
06 Oct '03 18:54
Phlabby, you've gone and rounded :'(.

Acolyte, you've demanded an answer that is cumbersome with just ASCII, so now Phlabby was forced to round his answer. Shame on you ðŸ˜›.

11. TheMaster37
Kupikupopo!
12 Oct '03 19:08
Originally posted by Acolyte
Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?

(Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC ðŸ˜³)
Square with sides 2, so the biggest circle in it has radius 1. On the diagonal of the square there is exactly sqrt(2)-1 left in the top left corner. The bit is the diagonal of a smaller square, with sides...sqrt(3/2 - sqrt(2)). So the cicle in there would have radius 1/2*sqrt(3/2 - sqrt(2)), wich is then the ratio of them.

Wich is also sqrt(2) / sqrt(3 - 2*sqrt(2)) : 1

I think...
12. Fiathahel
Artist in Drawing
13 Oct '03 14:36
Originally posted by TheMaster37
Square with sides 2, so the biggest circle in it has radius 1. On the diagonal of the square there is exactly sqrt(2)-1 left in the top left corner. The bit is the diagonal of a smaller square, with sides...sqrt(3/2 - sqrt(2)). So the cicle in there would have radius 1/2*sqrt(3/2 - sqrt(2)), wich is then the ratio of them.

Wich is also sqrt(2) / sqrt(3 - 2*sqrt(2)) : 1

I think...
Hmm, I don't see what you're doing, but ....

sqrt(2)-1 : sqrt(2)+1

Perhaps you might think now: WHY? so I'll give you my reasoning.

The ratio of the radii equals the ratio of the (2*radius+distance from circle to corner of the smallest square around the circle)s. These lengths are easy to compute. The numbers in the answer are those lengths if you start with a square with sides 2.
13. Phlabibit
Mystic Meg
13 Oct '03 16:42
Originally posted by Fiathahel
Hmm, I don't see what you're doing, but ....

sqrt(2)-1 : sqrt(2)+1

Perhaps you might think now: WHY? so I'll give you my reasoning.

The ratio of the radii equals the ratio of the (2*radius+distance from circle to corner of the smallest square around the circle)s. These lengths are easy to compute. The numbers in the answer are those lengths if you start with a square with sides 2.
That small circle won't fit inside the square if you use the distance from the circle to the corner as the diameter.....

P
14. Acolyte
Now With Added BA
13 Oct '03 17:03
Phlabibit and Fiathahel's answers sound about right, but I'm not sure about the reasoning. Could you elaborate?
15. royalchicken
CHAOS GHOST!!!
13 Oct '03 17:351 edit
Fiathahel's answer is the same as 3-2sqrt(2), or about 0.17, which is what I got. They can explain themselves though ðŸ™‚