If we have a circle of radius $R$ around center $O$ and its inscribed triangle $XYZ$ that is acute as well as scalene. $XY$ is the longest side. $XA,YB, ZC$ are the altitudes of the triangle $XYZ$. Let $L$ be the symmetric point of $A$ w.r.t. $BC$ and $M$ be the symmetric point of $B$ in $AC$. $P$ is the intersection of $XL$ and $YM$. $H$ is the orthocenter of triangle $XYZ$.
Then $OP\cdot OH = f(R)$. Find $f(R)$.