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No.No.No.No.
If a parallelogram is inscribed in a circle then it must be a cyclic quadrilateral.
You cannot circumscribe a "true rhombus". The opposite angles of a circumscribed quadrilateral must be supplementary whereas the opposite angles of a rhombus must be equal. That means a circumscribed rhombus is really a square.
To circumscribed a circle about a triangle you use the angle. This is to get the right measurements.
circumscribed about