AB is the diameter of a circle centered at the point O. BC is a chord.

AB is the diameter of a circle centered at the point O. BC is a chord. The angle AOC is known to be 130 degrees. Find the angles of the triangle BOC.

Determine the value of the angle BОС.

The angle AOB is expanded and is equal to 180, then the angle BOC = 180 – AOC = 180 – 130 = 50.

Consider a triangle BCO, in which OC = ОB, as the radius of the circle, therefore the angles OCB and ОBС are equal, since the angles at the base of an isosceles triangle are equal.

Then the angle OCB = (180 – COB) / 2 = (180 – 50) / 2 = 65.

Answer: The angles of the triangle BОС are equal: ∠СОB = 50, ∠ОСВ = ∠ОВС = 65.