examday

/TMUA

$A,B$ and $C$ are three points on a regular $n$-sided polygon, where $n\ge3$. Let $O$ be the centre of the circle that has $A,B$ and $C$ on its circumference. In radians, $\angle AOB=\frac56\pi$ and $\angle BOC=\frac25\pi$. Then $n$ is necessarily a multiple of $k$. What is the largest value of $k$ such that this statement is true?