# 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.

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