# Thread: A very hard word problem

1. ## A very hard word problem

There is a cycle- shaped area, with grass. In any point of the cycle there is a cow tighten with a rope.How long should the rope be, that the cow can eat half of the grass in the cycle ?

I hope u understand, because I've read it in another language and I tried to put it in english

2. Originally Posted by alternative
There is a cycle- shaped area, with grass. In any point of the cycle there is a cow tighten with a rope.How long should the rope be, that the cow can eat half of the grass in the cycle ?

I hope u understand, because I've read it in another language and I tried to put it in english
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 = $2 \pi r$
Within this circle, you have a cow, attached by a rope, to the fence. You want the cow to be able to reach exactly $\frac{\pi r^2}{2}$ 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 = $\frac{\pi r^2}{2}$, 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..