Ex. 20. In a circle, two chords $A C$ and $B D$ are drawn, intersecting at an angle of $60^{\circ}$. It is known that lines $A B$ and $C D$ are parallel and two sides of the quadrilateral $A B C D$ are equal to 3. Find the radius of the circle.
Ex. 20. Answer: $3, \sqrt{3}$. Solution. There are 4 possible arrangements of the vertices of the quadrilateral on the circle:
![](https://cdn.mathpix.com/cropped/2024_05_21_91ff4e46083e03d62f1eg-31.jpg?height=310&width=1328&top_left_y=1208&top_left_x=364)

In each of these cases, the generalized sine theorem is used to find the radius.