# Playing with circles and triangles

Calculus Level 5

In a unit circle with centre $$O$$ two points $$A$$ and $$B$$ are taken on the circumference of the cirlce. Then the inradius of the triangle $$OAB$$ is $$r$$. If the maximum value of $$r$$ is $$\alpha$$, what is $$\lfloor 1000\alpha \rfloor$$?

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