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)

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?

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)

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.

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.

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.

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.

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 ....

The answer is:

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.

Originally posted by Fiathahel Hmm, I don't see what you're doing, but ....

The answer is:

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.....