## Task 14/89

Given a parallelogram $A B C D$ with $E$ as the midpoint of side $C D$. In what ratio does the line segment $B E$ divide the diagonal $A C$?
Let $M$ be the diagonal intersection of the parallelogram. We consider the triangle $D B C$. In it, $C M$ and $B E$ are medians ($C M$: In a parallelogram, the diagonals bisect each other; $B E$: by assumption).

If $S$ is the intersection of the medians, then $C S: S M=2: 1$ (according to the theorem "In a triangle, the intersection of the medians divides them in the ratio $2: 1$"). Then we have

$$
C S: S A=2:(1+3)=2: 4=1: 2 \quad \text { or } \quad A S: S C=2: 1
$$

This means that $B E$ trisects the diagonal $A C$.