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 as

![](https://cdn.mathpix.com/cropped/2024_05_06_2124392d30f110fb249eg-2.jpg?height=403&width=459&top_left_y=204&top_left_x=1204)

one triangle (for example, AOB and BOA).

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 $120^{\circ}$.