In triangle ABC, angle B = 60 degrees. Point O is marked inside the triangle

In triangle ABC, angle B = 60 degrees. Point O is marked inside the triangle, equidistant from its vertices. Prove that the AOC triangle is obtuse.

Point O is the center of a circle circumscribed about ABC triangle.

The inscribed angle ABC rests on the arc AC, the degree measure of which is equal to two values of the angle ABC. Arc AC = 2 * 60 = 120.

The central angle AOC is also based on the arc AC, and therefore its value is equal to the degree measure of the arc AB.

Angle AOC = 120, as required.