Question 27
The quadrilateral $ABCD$ is inscribed in the circle $k$. The lines $AC$ and $BD$ meet in $E$ and the lines $AD$ and $BC$ meet in $F$. Show that the line through the incenters of $\triangle ABE$ and $\triangle ABF$ and the line through the incenters of $\triangle CDE$ and $\triangle CDF$ meet on $k$.