3. $A B C D E F$ - a regular hexagon, point O - its center. How many different isosceles triangles with vertices at the specified seven points can be constructed? Triangles that differ only in the order of vertices are considered the same (for example, AOB and BOA).

![](https://cdn.mathpix.com/cropped/2024_05_06_9f0e99362a618937dfe0g-2.jpg?height=403&width=459&top_left_y=204&top_left_x=1204)

ANSWER: 20.
Solution: First, consider the triangles that do not contain point O. These are two equilateral triangles and 6 triangles with an angle of $120^{\circ}$. With vertex $O$, there are 6 equilateral triangles and 6 triangles with an angle of $120^{\circ}$.