# Grazing In A Circular Pen

Calculus Level pending

A leash of length $$L$$ is secured to the side of a circular pen of radius $$r = 100\text{ m}$$ so that the region accessible from the free end of the leash is half of the area of the pen.

What is the length $$L$$ of the leash to the nearest meter?

Assume $$100 \text{ m} < L < 141 \text{ m}$$.

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