[Thales' Theorem and the Proportional Segments Theorem]

On the median $A M$ of triangle $A B C$, a point $K$ is taken such that $A K: K M=1: 3$.

Find the ratio in which the line passing through point $K$ parallel to side $A C$ divides side $B C$.
Let the line mentioned in the problem intersect side $B C$ at point $N$. By the theorem of proportional segments,

$M N: N C = M K: K A = 3: 1$, hence, $M N = 3 N C, B N = B M + M N = C M + M N = 7 N C$.

## Answer

## $1: 7$.