Answer:
In a circle, an angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the circle.
Given that \( \angle AOB = 60^\circ \) (angle subtended at the center), \( \angle CDB = 90^\circ \) (a right angle subtended at the circumference), we can find \( \angle OBC \).
\( \angle OBC \) is half of \( \angle CDB \) since they both subtend the same arc:
\[ \angle OBC = \frac{1}{2} \times \angle CDB = \frac{1}{2} \times 90^\circ = 45^\circ \]
Therefore, \( \angle OBC \) is \( 45^\circ \).
