Let \(O\) be the circumcenter of \(ABC\). Reflect \(O\) over \(BC\) to obtain \(O'\). Through \(O'\) construct lines parallel to \(AC,AB\) which respectively meet \(AB,AC\) at \(F,E\). Define \(O'F\cap OB=Y, O'E\cap CO=X\). Prove \(XY||EF\)
I personally think this configuration is very rich and can be exploited to create difficult olympiad geo problems.