Geometry Level 3

In $$\triangle ABC$$, $$AD$$ is the perpendicular from $$A$$ onto $$BC$$, $$BE$$ is the median and $$CF$$ is the internal angle bisector of $$\angle ACB$$ such that $$D$$ is on $$BC$$ , $$E$$ on $$AC$$ and $$F$$ on $$AB$$. Suppose that $$AD$$ , $$BE$$ and $$CF$$ are concurrent. If $$FE = ED = 6$$ unis, find

$$\large{\dfrac{R_{AEF} + R_{FBD} + R_{EDC} + R_{DEF}}{R_{ABC}}}$$

Details and assumptions : $$R_{XYZ} =$$ length of the circumradius of $$\triangle XYZ$$

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