Question

If there are two farmers who have grown grass in the circular field then what should be length of rope so that equal crop is distributed to both if rope is tied at the center of the circular field if r is radius of the circle

Answer 1

You want a circle of radius a inside the circle of radius r, so that

pi r^2 = 2pia^2
2a^2 = r^2
a = r/√2