# Inspired by Rama Devi

Calculus Level 5

There are 3 concentric circles with center $$O$$ and radii $$3,5,7$$ units. Points $$A,B,C$$ are respectively on these circles, one on each circle.

When $$AB^2+BC^2+CA^2$$ is maximized, what is the value of $$\sin \angle AOB$$ (to 3 decimal places)?

Inspiration

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