Hollow Circle at the edge!

Consider a ring which mass is standard distributed .

The ring is place at one corner of the table as the picture shown above.

What is the minimum ratio of area \(\frac{A}{B}\) when the ring is just going to fall from the corner?

If the answer can be represented by \(\frac{a\pi -b}{c\pi+d}\) which \(a,b,c,d\) is positive integer and the fraction is the simplest form. Then find \(a+b+c+d\).

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