a circular field of 7km radius is divided by 3 brothers in such a way that the eldest get the area of circular field which is outside the largest equilateral triangle which can be fitted in the circular field.the youngest gets the largest circular area which can be fitted in that circular area which can be fitted in that equilateral triangle.what will be the share of second brother?

• The radius of the outer circle, the circumcircle of the equilateral triangle, is 7.
  So, the circum radius of the equilateral triangle is 7. So, the altitude of the equilateral triangle is 3*7/2= 21/2.
  The area of the equilateral triangle can be written as (root 3)/4 S^2 or it can be written as (altitude)^2/(root 3) . So, the area of the equilateral triangle is 441/4(root 3)= 63.65
  The innere circle is the incircle of the equilateral triangle, so its radius, the inradius, is half of the circum radius, that is 7.
  So, radius =3.5 Area =22/7 *3.5 *3.5=38.5
  
  Share of the middle brother = 63.65-38.5=25.15
  
  Answer is 25.15
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