Radiohead (2+2=5)

The altitudes $BE$ and $CF$ of a triangle $ABC$ meet at $H$ . The extensions of $FE$ and $BC$ meet at $U$ . A line through the midpoint $L$ of $BC$ parallel to the internal bisector of $\angle{EUB}$ meets $CA, AB, HC, HB$ (extended as necessary) at $P, Q, X, Y$ , respectively. If the circumradius of $APQ$ is $r_{1}$ and the circumradius of $HXY$ is $r_{2}$ , find $\dfrac{r_{1}}{r_{2}}$ .

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