Let $ABC$ be an acute triangle with circumcenter $O$. The altitude from $A$ meets $BC$ at $D$. The line through $D$ parallel to $AO$ meets $AB$ at $E$ and $AC$ at $F$. Prove that $OE = OF$.
To illustrate the quality, here is a classic problem translated from a 2015 PDF: cuban mathematical olympiads pdf
Most files are written in Spanish . However, for math olympiad training, this is a minimal barrier because: Let $ABC$ be an acute triangle with circumcenter $O$