In figure OM ⊥ BC
∴ ∠OMC = 90°
and ∠BCO = 30°
∠AOD = 90° (from figure)
∴ ∠OMC = ∠AOD = 90° (corresponding angles)
∴ BC || OD
∴ ∠COD = ∠BCO (alternate angles)
∴ ∠COD = 30°
By arc CD, angle subtend at center ∠COD is double the angle at remaining part of circle ∠CBD.