geometry

 

   A circle is inscribed in a square as shown above.     

   A smaller circle is drawn tangent to two sides of the square and externally tangent to the inscribed circle.     

   Find the area of the blue shaded region.     

 

   A_square  =  10²  =    100.00     

   A_{big circle}  =  π 5²  =  78.54     

   A_{four corners}  =           21.46     

   A_{one corner}  =  21.46 / 4  =  5.365     

 

   Diagonal_square  =  10 sqrt(2)  =  14.142     

   Diameter_{small circle}  =  (14.142 / 2) – 5.000  =  2.071     

   Radius_{small circle}  =  2.071 / 2  =  1.0355     

 

   Area_{one corner} (from above)          =  5.365     

   Area_{small circle}  =  π 1.0355²         =  3.369     

   Area of Interest (by subtraction)  =  1.996  round to  2     

   _.