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# Largest square that fit inside a circle

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8 replies to this topic

### #1P0jahn  Members

Posted 17 March 2013 - 12:41 PM

I want to calculate the width/height of the largest square that fits inside this circle.

### #2C0lumbo  Members

Posted 17 March 2013 - 12:57 PM

I think the answer is that the side of the squares are (radius * root2) = 1.414213 * radius.

I suck at showing working, but the trick was to imagine the right-angled triangle made where the radius at 45-degrees is the hypotenuse, and the other two sides represent half the square edge length.

### #3P0jahn  Members

Posted 17 March 2013 - 01:01 PM

Thanks for the help.

Although I have to apologize for not understanding your anwser.

I have a 2nd question that is related to this:
How do I calculate the position of the unknown position?

Edited by P0jahn, 17 March 2013 - 01:02 PM.

### #4SimonForsman  Members

Posted 17 March 2013 - 01:10 PM

Thanks for the help.
Although I have to apologize for not understanding your anwser.

I have a 2nd question that is related to this:
How do I calculate the position of the unknown position?
question2.png

the center of the square would be at:

your unknown corner is then located at:

ux = cx + cos(3PI/4) * radius
uy = cy + sin(3PI/4) * radius

The length of the side of the square is 2 * cos(3PI/4) * radius

Edited by SimonForsman, 17 March 2013 - 01:13 PM.

I don't suffer from insanity, I'm enjoying every minute of it.
The voices in my head may not be real, but they have some good ideas!

### #5P0jahn  Members

Posted 17 March 2013 - 01:26 PM

Thanks. What does 3PI means? Or is it just PI?

### #6SimonForsman  Members

Posted 17 March 2013 - 01:28 PM

Thanks. What does 3PI means? Or is it just PI?

3 * PI
I don't suffer from insanity, I'm enjoying every minute of it.
The voices in my head may not be real, but they have some good ideas!

### #7Tournicoti  Prime Members

Posted 17 March 2013 - 02:03 PM

@OP : this is not just 3*Pi but 3*Pi/4  (so 3*Pi is needed)

### #8Michael Tanczos  Staff Emeritus

Posted 17 March 2013 - 05:11 PM

Thanks for the help.

Although I have to apologize for not understanding your anwser.

I have a 2nd question that is related to this:
How do I calculate the position of the unknown position?

You need to take the square you want to create and split it into two triangles along the diagonal.   This diagonal would be the same as the diameter of the circle.  To figure out the sides you just need the quadratic equation: a2 + b2 = c2 .    Well c2 is the diameter.. that much should be known.. and both sides will be equal.  So a2 = b2, making it sufficient to change the equation to 2a2 = c2.. or basically side = sqrt(diameter2 / 2).  Or in terms of the radius, side = sqrt(2r2)

Or as C0lumbo reduced it even further:

side = sqrt(2) * r

side = 1.414213 * r

Edited by Michael Tanczos, 17 March 2013 - 09:48 PM.

### #9P0jahn  Members

Posted 17 March 2013 - 05:48 PM

Thanks all!

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