Line AB touches a circle with center O at point B. Find OA if AB = 2√3, and angle A is 30 degrees.

From the condition it is clear that AB and the center of the circle O form a right-angled triangle.
In which AB is a leg, BO is a leg, and OA is a hypotenuse.
Find the hypotenuse, write down the formula for finding:
ОА = AB / (cos 30 °);
Substitute the values and calculate:
OA = 2√3 / (√3 / 2);
OA = 2√3 * 2 / √3;
OA = 4.
Answer: 4