A chord BC is drawn in a circle centered at point O. Determine the angles ОBС and ОBС if the angle BОС = 86 degrees.

The segments connecting the center of the circle with the extreme points of the chord are equal as the radii of the circle:

OB = OC.

If the two sides of the triangle OBC are equal, then it is isosceles and opposite the equal sides are equal angles OBC and OCB.

<BOC + <OBC + <OCB = 180 ° (the sum of the angles of the triangle is 180 °).

<OBC + <OCB = 180 ° – <BOC = 94 °;

<OBC = <OCB = 94 ° / 2 = 47 °.

Answer: <OBC = <OCB = 47 °.