No need of any jugglery

Geometry Level 3

Given is an equilateral \(\Delta ABC\). \(BE\) is parallel to \(AC\) and intersects \(AD\) produced at \(E\) where \(D\) is the midpoint of \(BC\). \(F\) is the midpoint of \(BD\). Find the ratio of radius of circle circumscribing \(\Delta CDE\) to that of the circle circumscribing \(\Delta ADF\). Provide your answer up to three decimal places.

The problem is original. You may also try this one.
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