B1. Circles $\mathcal{K}_{1}$ and $\mathcal{K}_{2}$ in the figure are the circumcircle and incircle of an equilateral triangle $A B C$. Circle $\mathcal{K}_{2}$ has a square $D E F G$ inscribed in it, with point $D$ lying on side $A B$. Circles $\mathcal{K}_{3}$ and $\mathcal{K}_{4}$ are of equal size and touch each other, and each touches two sides of the square $D E F G$. Determine the ratio of the radii of circles $\mathcal{K}_{1}$ and $\mathcal{K}_{4}$.

(6 points)

![](https://cdn.mathpix.com/cropped/2024_06_07_58dcb28c79ea4cc315e1g-07.jpg?height=643&width=603&top_left_y=198&top_left_x=1252)