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Square in a circle

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Suppose i have a circle. I cut off its arcs such that it became the biggest possible square i could make from that circle.  What's the ratio of the edge of the circle to the middle of the edge of the square (assume minimum length) to the radius of the circle. 

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Suppose i have a circle. I cut off its arcs such that it became the biggest possible square i could make from that circle.   This is clear

Several clarifications are required:    What's the ratio of the edge of the circle .....(1)  edge of the circle  a) the circumference    or b)  one of the arcs

clarification required:  to the middle of the edge of the square   ?                         (assume minimum length) to the radius of the circle. 

 . Is the question : What is the ratio of the arc length   to the perpendicular length from the center of one side of the square to the arc ???

 

 

Suppose i have a circle. I cut off its arcs such that it became the biggest possible square i could make from that circle.  What's the ratio of the edge of the circle to the middle of the edge of the square (assume minimum length) to the radius of the circle. 

 

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If the question is : What is the ratio of the arc length   to the perpendicular length from the center of one side of the square to the arc ??? 

Then assuming diameter of 1" ; the diagonal of the largest square would also be  1 ; this divides the square into  2 isosceles triangles ,whose angles are 45,45,90   In a 45 degree triangle the sides are = Hsin angle  or 1 sin 45 = 0.707;  therefore i/2 of the lt of a side is 0.353 .    The radius is 0.5.   0.5 - 0.353 = the rise  0.147  the distance from arc to square

 Now the circumference  is pie D or 3.14 D,  3.14 (1) = 3.14;  acr length 3.14 divided by 4 =0.7853  ratio of arc length to rise  ....0.7853/0.147 =  5.342 :1

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Spoiler

Assume the radius R = 1. The diagonal of the square will be 2R = 2. The sides of the square will be sqrt(2). The length from the center to the midpoint of the square's side is sqrt(2)/2. The ratio is then (1-sqrt(2)/2) / 1, or just 1 - sqrt(2)/2, or about 0.3.

 

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Maybe one of you answered this question:  :)

I should have included this pic though...

 

 

circle puzzle.png

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