In a circle centered at point O, AB is a diameter. If chord AC creates a 60° angle at the center, then the measure of \(\angle\)OCB will be:

Q.In a circle centered at point O, AB is a diameter. If chord AC creates a 60° angle at the center, then the measure of \(\angle\)OCB will be: (a) 20° (b) 30° (c) 40° (d) 50°

Answer: B

AC is a chord that produces a 60° angle at the center. \(\therefore \angle AOC = 60^\circ\) \(\therefore \angle COB = 180^\circ - 60^\circ = 120^\circ\) Now, in triangle COB, OB = OC (as both are radii of the circle) \(\therefore \angle OCB = \cfrac{180^\circ - 120^\circ}{2} = 30^\circ\)