7. A point $M$ is chosen on the diameter $A B$.

Points $C$ and $D$, lying on the circle on the same side of $AB$ (see figure), are chosen such that $\angle A M C = \angle B M D = 30^{\circ}$. Find the diameter of the circle if it is known that

![](https://cdn.mathpix.com/cropped/2024_05_06_35052e7d512455511f98g-06.jpg?height=677&width=725&top_left_y=2137&top_left_x=1154)
$C D=12$.
Answer: $8 \sqrt{3}$.

Solution: Let's make a symmetry relative to the diameter. We get that arcs CD and $\mathrm{C}_{1} \mathrm{D}_{1}$ are equal, and their sum is $240^{\circ}$, so each arc is $120^{\circ}$. We can consider, for example, that $\mathrm{CD}$ is a side of an inscribed equilateral triangle and find the radius $R=4 \sqrt{3}$.