5.2.4.4 Various problems on the plane

On the base \( B C \) and the side \( C D \) of the trapezoid \( A B C D \), points \( M \) and \( N \) are taken. The segments \( A M \) and \( B N \) intersect at the point \( K \). It is known that \( A K=3 K M, K N=2 B K \). In what ratio does the point \( N \) divide the side of \( C D \) ?