CGMO 2013 Problem 7

As shown in the figure, $\odot O_1$ and $\odot O_2$ touches each other externally at a point $T$ , quadrilateral $ABCD$ is inscribed in $\odot O_1$ , and the lines $DA$ , $CB$ are tangent to $\odot O_2$ at points $E$ and $F$ respectively. Line $BN$ bisects $\angle ABF$ and meets segment $EF$ at $N$ . Line $FT$ meets the arc $\widehat{AT}$ (not passing through the point $B$ ) at another point $M$ different from $A$ . Prove that $M$ is the circumcenter of $\triangle BCN$ .

Attachments: