Within a farmer's pastures, there is a one-acre tract of land shaped like a right triangle. At the midpoint of the hypotenuse is a post, to which a dog is tethered with just enough rope to reach the endpoints of the hypotenuse. There are also posts at the midpoints of the legs of the triangle; to each of which is tethered a sheep with just enough rope to reach the endpoints of its respective leg of the triangle.

How much space do the sheep have to graze in (collectively) without having to worry about the dog reaching them?

(In reply to Solution by Benjamin J. Ladd)

The triangular one-acre tract is not the whole pasture. Both the dog and the sheep are free to travel through their whole circles, not just the semicircles that are within the triangle. At least, that's the reading of the people who come up with non-zero answers.

Posted by Charlie on 2003-11-15 22:09:39