# Largest square that fit inside a circle

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P0jahn    307

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

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C0lumbo    4411

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.

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P0jahn    307

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?

[attachment=14316:question2.png]

Edited by P0jahn

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SimonForsman    7642

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

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P0jahn    307

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

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SimonForsman    7642

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

3 * PI

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

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Michael Tanczos    5681

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

P0jahn    307

Thanks all!

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