I haven't got an answer at the mo, but just to check I'm reading it right -

You have a circular fence in a field. Let's assume that you know the length of the fence, so we have something to work in terms of.

Length of fence =

Within this circle, you have a cow, attached by a rope, to the fence. You want the cow to be able to reach exactly of the grass.

Is that the right idea?

If so, I'd suggest maybe considering the fact that the cow is at the centre of another circle, of radius q. When the area of the intersection of these two circles = , then q will be the length of rope you want.

Sorry I've only an idea, and not quite the answer...

It's an interesting problem though..