Half Rations

This issue's PASS Maths puzzle is an old favourite. To work out the answer you might end up with an equation you can't solve: but it's fine to use a calculator to give you an approximate solution if you like.

A grassy field is in the shape of a circle of radius 100m and is enclosed by a circular fence.

A goat is attached by a rope to a hook, at a fixed point on the fence.

To stop the goat getting too fat, the farmer wants to make sure that it can only reach half of the grass in the field.

How long should the rope be?