Line Through the Incircle Center of a Tangential Quadrilateral

A convex quadrilateral $ABCD$ is circumscribed about a circle $O$; that is, each of its four sides is tangent to the circle. A line through $O$ meets the sides $AB$ and $CD$ at $K$ and $L$, and meets the diagonals $AC$ and $BD$ at $M$ and $N$, respectively. Suppose that $\angle BKL=\angle CLK$, $AM=1$, $MC=2$, and $BN=3$.

Find $ND$.