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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