2. (7 points) In rectangle $A B C D$, side $A B$ is equal to 6, and side $B C$ is equal to 11. Bisectors of the angles from vertices $B$ and $C$ intersect side $A D$ at points $X$ and $Y$ respectively. Find the length of segment $X Y$.

![](https://cdn.mathpix.com/cropped/2024_05_06_2509cbb2376df96befe7g-1.jpg?height=317&width=417&top_left_y=1121&top_left_x=822)

## Answer: 1.