A goat is tethered to the perimeter fence of a circular field by an inelastic rope.
Assume:

1. that the mouth of the goat can reach no further from the tethering point than the length of the tethering rope, and

2. that the tethering point on the perimeter of the field is fixed, and

3. that there is only the one animal grazing in the circular field, and

4. that the grass grows uniformly over the surface area of the field,

What is the length of the rope if the goat can eat exactly 50% of the grass in the field?

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