4. A triangle with sides 2, 3, and 3 was cut into four triangles similar to it. What could the similarity coefficients be?
Answer: $1 / 2$ and $6 / 13, 4 / 13, 9 / 13, 6 / 13$.

Solution: Note that the only arrangement of four triangles so that they are similar to the larger one (and thus to each other) is such that each triangle has one vertex at a vertex of the larger triangle and the other two on its sides, with one point marked on each side of the larger triangle ($A^{\prime}$ on $B C, B^{\prime}$ on $A C, C^{\prime}$ on $\left.A C\right)$. Then there are exactly two options - $\angle C A^{\prime} B^{\prime}=\angle C A B$ and $\angle C A^{\prime} B^{\prime}=\angle C B A$. The other angles are uniquely determined. Both options give a set of four similar triangles.

Criteria: $\mp$ - only the first variant is considered.