Circumradius Party!

Geometry Level pending

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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