Possible Duplicate:
The cow in the field problem (intersecting circular areas)
A farmer ties a cow with a rope to a pole at the edge of a round field of radius r. How long must the rope be compared to r if the farmer wants to ensure that the cow can roam exactly half of the field?
The point is to find a closed-form expression, not solve this with numerical analysis etc. Is that possible?
There's a nice depiction of the problem here: _http://www11.speedyshare.com/files/25162122/download/Cow.png