2. In triangle $A B C$, $|A C|=6,|B C|=2$ and $\angle A C B=120^{\circ}$. The angle bisector of $\angle A C B$ intersects side $\overline{A B}$ at point $D$. Determine the length of segment $\overline{C D}$.
2. Let $E$ be a point on the line $A C$ such that $C$ is between $A$ and $E$, and $|C E|=|C B|$.

![](https://cdn.mathpix.com/cropped/2024_05_30_ad525663fbc4e6951048g-02.jpg?height=226&width=674&top_left_y=2016&top_left_x=862)

5 points

Triangle $E C B$ is equilateral and $B E \| D C$, so from the similarity of triangles $A C D$ and $A E B$ we get

$$
\frac{|C D|}{|A C|}=\frac{|E B|}{|A E|} \text { i.e. }|C D|=\frac{3}{2}
$$

20 points