OPQR is a rhombus, three of whose vertices lie on a circle with centre O. If the area of the rhombus is 32 (under-root)3 cm2, find the radius of the circle.

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 Square is the only rhombus that can be cyclic. 

So here we have the area of the square ( that is the rhombus given in the question) 32 sqrt(3). This can be used to take out the length of one side.

Now You can use pythagoras to take out the diameter, as the diameter will be the diagonal of the square. 

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