We will use the circumference formula to find the original radius.

We know that:

C = 2*r*pi where r is the radius.

Given that the circumference is 75 m.

==> 75 = 2*r*pi

Now we will divide by 2pi.

==> r= 75/2pi = 11.94 m (approx.)

Now we know that the distance between the circle and the fence is 10 m.

Then the radius of the circular fence is r+ 10 = 11.94+10 = 21.94 m.

Now we will calculate the circumference of the fence given the radius 21.94.

==> C = 2*pi * r = 2*pi * 21.94 = 137.83 m

Then the length of the fence is 137.83 m

The circular barn has a circumference of 75 m. For a circle of radius r, the circumference is given as 2*pi*r

2*pi*r = 75 m

=> r = 75/2*pi

The fence has been constructed all around the barn at a distance of 10 m from it. This gives the radius of the circle formed by the fence as 10 + 75/2*pi

The length of the fence is 2*pi*(10 + 75/2*pi)

=> 20*pi + 75

The required length of the field is 20*pi + 75 or 137.83 m