The incircle of triangle $ABC$ touches $BC,CA,AB$ at $D,E,F$ respectively . The circle passing through $A$ and touching the line $BC$ at $D$ intersects $BF$ and $CE$ at points $K$ and $L$ respectively . The line passing through $E$ and parallel to $DL$ and the line passing through $F$ and parallel to $DK$ intersects at $P$ .
Let $R_1,R_2,R_3,R_4$ be circumradius of $\Delta AFD, \Delta AED , \Delta FPD , \Delta EPD $ . Find the value of $k$ for which $R_1R_4=k . R_2R_3$ .
relation among radiuses
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