Circle in square, calculate distance from square's corner to circle's perimeter? I have a square that is $33\times33$ cm. I will put a circle in it that has a diameter of $33$ cm. How do I calculate the distance from the square's corner to the circle's closest perimeter in a straight line? For example, the green arrow below shows what I want to know.

 A: The diagonal of the square is $33\sqrt 2$, so the green arrow is $\frac 12 (33\sqrt 2 -33)=\frac {33}2(\sqrt 2-1)\approx 6.835$
A: If Square is having side = s 
Now, Diagonal (D) can be calculated using Pythagorean theorem:
(D)'2 = (s)'2 + (s)'2
(D)'2 = 2 (s)'2
 D =  _/2 (s)
 D = 1.414 (s)
 D = 1.414 s
Since diameter of inscribed circle in square = side of square
Therefore, diameter of inscribed circle in square = s  
Thus,
The remaining distance beyond diameter of inscribed circle over diagonal of square  (X) = ( Diagonal of square - Diameter of inscribed circle )
It implies
 X = (1.414 s) - (s)
 X = 1.414 s - s 
 X = (1.414 - 1) s
 X = (0.414) s 
 X = 0.414 s
Hence,
The distance from the square's corner to the circle's closest perimeter in each side of a straight line/diagonal (Y)= 1/2 (X)
Y = 1/2 (X)
 Y = 1/2 (0.414)
 Y = 0.207
Dr. Sajad Ahmad Mir,
Physics,
Pampore, Srinagar, J&K, India-192121
A: If Square is having side = s ,
Now, Diagonal (D) can be calculated using 
Pythagorean theorem:
(D)'2 = (s)'2 + (s)'2 ,
(D)'2 = 2 (s)'2 ,
D =  _/2 (s), 
D = 1.414 (s) ,
D = 1.414 s ,
Since diameter of inscribed circle in square = side of square, 
Therefore, diameter of inscribed circle in square = s  
Thus,
The remaining distance beyond diameter of inscribed circle over diagonal of square  (X) = ( Diagonal of square - Diameter of inscribed circle ),
It implies, 
X = (1.414 s) - (s) ,
X = 1.414 s - s ,
X = (1.414 - 1) s ,
X = (0.414) s ,
X = 0.414 s, 
Hence,
The distance from the square's corner to the circle's closest perimeter in each side of a straight line/diagonal (Y)= 1/2 (X) ,
Y = 1/2 (X) ,
Y = 1/2 (0.414) ,
Y = 0.207
Dr. Sajad Ahmad Mir,
Physics,
Pampore, Srinagar, J&K, India-192121
