From point $A$ to point $C$, there is an educational trail passing through point $B$, and there is also a red tourist trail, see the image. In addition, a shortcut not shown in the image can be used, which is 1500 meters long, starting at $A$ and ending on the educational trail. Vojtěch found that

1. the trip from $A$ along the red trail to $C$ and back along the educational trail to $A$ is 7700 meters long,
2. the trip from $B$ along the educational trail to $C$ and then along the red trail to $A$ is 5800 meters long,
3. using the shortcut, the trip from $A$ to $B$ is 1700 meters long,
4. the trip from $A$ along the educational trail to $C$ and back to $A$ first along the educational trail and then along the shortcut is 8800 meters long.

Determine the length of the educational trail from $A$ to $C$. If the problem allows multiple answers, provide all of them.

(L. Simünek)

![](https://cdn.mathpix.com/cropped/2024_04_17_5752a8a8cd9a6cffa1f9g-2.jpg?height=556&width=552&top_left_y=967&top_left_x=752)

Hint. Determine where the shortcut could end on the educational trail.