The central angle AOB rests on a chord AB of length 5. The angle OAB is 60 °. Find the radius of the circle.

If the angle AOB is central, then the segments AO and OB are equal and are the radii of the circle. So triangle AOB is isosceles. And in an isosceles triangle, the angles at the base are equal.

If the angle AOB is 60⁰, then the angles OAB and OBA in total are 180 – 60 = 120⁰

It turns out that the angle OAB = angle OBA = 60⁰, that is, the triangle AOB is equilateral. So the length of the radius is 5.