# Locus of the Incenter

Geometry Level 5

Let $$\mathbf{P}$$ be the locus of the incenters of all possible right triangles with a common hypotenuse. If the length of this common hypotenuse is $$1$$, and the area locus $$\mathbf{P}$$ encloses is $$A$$, then find $\lfloor 1000A\rfloor$

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