A circle centered at point O is described around an isosceles triangle ABC, in which AB = BC

A circle centered at point O is described around an isosceles triangle ABC, in which AB = BC and angle ABC = 49. Find the BOC angle.

The inscribed angle ABC = 49 and rests on the arc AC, then the degree measure of the arc AC = 2 * ABC = 2 * 49 = 98.

Since the triangle ABC is isosceles, the chord AB = BC, and hence the arc AB = BC.

The sum of arcs AC + AB + BC = AC + 2 * BC = 360.

2 * BC = 360 – 98 = 262.

BC = 262/2 = 131.

Then the value of the central angle BОС is equal to the arc ВС on which it rests.

BOC angle = 131.

Answer: The BOC angle is 131.