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?*