The central angle AOB rests on the chord AB of length 6. At the same time, the angle OAB is 60

The central angle AOB rests on the chord AB of length 6. At the same time, the angle OAB is 60 Find the radius of the circle.

The corner AOB is formed by two radii since it is inscribed, that is, OA = OB. It follows from this that the angles OAB and OBA are equal to each other.

By the condition of the problem OAB = 60, which means OBA = 60. Now we find the angle AOB. The sum of all angles in a triangle = 180 degrees, that is:

1) AOB + 60 + 60 = 180;

2) AOB = 180 – 120;

3) AOB = 60;

Since AOB = OAB = OBA = 60, then triangle AOB is equilateral, and all its sides are equal. The radius is 6.