A tangent AB is drawn through point A of the circle with center O. Find the radius of the circle

A tangent AB is drawn through point A of the circle with center O. Find the radius of the circle, if OB = 6, the angle AOB = 60 degrees.

The tangent is perpendicular to the radius, which means that the triangle OAB is right-angled, and OB is its hypotenuse;

Angle ABO = 180 – 60 – 90 = 30 °;

OA leg, which lies opposite an angle of 30 °, is equal to half of the hypotenuse, since sin (30 °) = 1/2;

Circle radius OA = 6/2 = 3.