Task B-2.4. The length of the side of a regular hexagon $A B C D E F$ is $a$. The lines $A B$ and $C D$ intersect at point $T$. Determine the distance $|F T|$.
First solution. Sketch

![](https://cdn.mathpix.com/cropped/2024_05_30_7c0a9615fb5cd46ea1c5g-08.jpg?height=585&width=767&top_left_y=496&top_left_x=663)

Triangle $BCT$ is equilateral (its angles are equal to the internal angles of a regular hexagon). The leg $FD$ is the shorter diagonal in a regular hexagon and is perpendicular to the line $CD$, so triangle $FDT$ is a right triangle.

(1 point)

The length $FT$ is its hypotenuse, and its length is

$$
(|FT|)^{2}=(a \sqrt{3})^{2}+(2a)^{2}
$$

Thus, $|FT|=a \sqrt{7}$.