Isosceles triangles $E O F, G O H$ and $E F G$ are similar.

## Otвет

$3: 1$.

## Answer

$3: 1$.
When triangle $E F G$ is rotated by an angle $\arccos _{1 / 3}$ around point $O$, which lies on side $E G$, vertex $F$ moves to vertex $E$, and vertex $G$ moves to point $H$, which lies on side $F G$. Find the ratio in which point $O$ divides side $E G$.