Solution:
Given, A, B, C are three points on a circle with center O such thatand .
Construct a figure according to the given data,
Here,
But ∠AOC is at the center made by are AC and ∠ABC at the remaining part of the circle.
Angle subtended by the arc at the center is double the angle subtended by it at any point on the circle.
Hence, the measure of ∠AOC is .
Therefore, option 2 is correct.