# Seeu Sim's Leg

Calculus Level 5

The above is a GIF showing the mechanism of a very simple but impractical leg. However, in maths, nothing is impractical.

It is known that the red colour circle above is of radius $$1$$.

The coordinates of the purple point are $$(0,-3)$$.

And the length of the black line (or leg) is $$5$$.

The green egg-shaped shape traces the path of the bottom of the black leg.

Given that the area of the green egged-shaped shape is $$A$$, find $\left\lfloor 1000A \right\rfloor.$

To be fair, you may use a computational method.

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