Question 97
The point $O$ is the circumcentre of triangle $ABC$. The point $E$ is on the extension of the side $AB$ such that $B$ is between $E$ and $A$, the point $F$ is on the extension of the side $AC$ such that $C$ is between $F$ and $A$, and the lines $BF$ and $CE$ intersect on the circumcircle of triangle $ABC$. The midpoint of $EF$ is $M$, and $N$ is a point on the circumcircle of triangle $ABC$ such that $|MN| = |EM|$. Prove that the angle $\angle MNO$ is a right angle.