From point $M$, tangents $M A$ and $M B$ are drawn to a circle with center $O$ (where $A$ and $B$ are the points of tangency). Find the radius of the circle if $\angle A M B=\alpha$ and $A B=a$.
Segment $O M$ is perpendicular to chord $A B$, bisects it, and $\angle O A B=\alpha / 2$.

## Answer

$a / 2 \sec \alpha / 2$.