Question 30
Circles $\omega_1$ and $\omega_2$ touch at point $K$. The line through the centres of the circles intersects the circle $\omega_1$ once more at point $A$. A line through the point $A$ intersects the circle $\omega_1$ once more at point $B$ and the circle $\omega_2$ at points $C$ and $D$, where the points $A, B, C, D$ lie on the line in the order. Given that the line segments $AB$, $BC$ and $CD$ have equal lengths, find the ratio of the radii of the circles $\omega_1$ and $\omega_2$.