15 Oct '07 18:10

This is an old one that I posted a few years ago, but I don't remember it being answered analytically (not sure if it's possible or not). So here we go again!

A farmer owns a circular field, and wants to put his goat in it. However, he only wants to allow the goat to graze over half the field (i.e. he's a sadist). If the goat is tied to the edge of the circular field, how long should the rope be to allow the goat to graze over half the field? Give your answer as a fraction of the diameter.

PS - This is easily solvable numerically, but can anyone come up with an analytical solution?

A farmer owns a circular field, and wants to put his goat in it. However, he only wants to allow the goat to graze over half the field (i.e. he's a sadist). If the goat is tied to the edge of the circular field, how long should the rope be to allow the goat to graze over half the field? Give your answer as a fraction of the diameter.

PS - This is easily solvable numerically, but can anyone come up with an analytical solution?