Diameters AD and BC are drawn in a circle centered at point O, the angle OCD is 30 °. Find the angle OAB.

Segments OS and OD are the radii of the circle, then the triangle COD is isosceles, which means that the angle COD = (180 – 30 – 30) = 120.

Angle AOB = COD = 120, since they are vertical.

The segment ОА = ОВ as radii, then the triangle AOB is isosceles, which means that the angle ABO = BAO = (180 – 120) / 2 = 30.

Answer: The angle OAB is 30.

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