[ Properties of medians. The centroid of a triangle.]

Given triangle $A B C$. On the extension of side $A C$ beyond point $C$, point $N$ is taken such that $C N=A C$; point $K$ is the midpoint of side $A B$.

In what ratio does the line $K N$ divide side $B C$?
Let $M$ be the point of intersection of lines $K N$ and $B C$. In triangle $A B N$, segments $B C$ and $N K$ are medians. Therefore, $B M$ : $M C=2: 1$

![](https://cdn.mathpix.com/cropped/2024_05_06_04ea0aec75eb28164af1g-18.jpg?height=343&width=857&top_left_y=1672&top_left_x=612)

Answer

$2: 1$, measured from point $B$.