Point O is the center of the circle on which points A, B and C lie. It is known that the angle ABC

Point O is the center of the circle on which points A, B and C lie. It is known that the angle ABC = 75 degrees and the angle OAB = 67 degrees. find the angle BCO.

ABCO is a quadrangle, while the distances from the center of the circle to each point are equal, since all these segments are the radii of the circle on which the points lie:

ОА = ОВ = ОВ = R.

Let’s break the figure into 2 triangles: ABO and BOС. Both triangles are isosceles. According to the properties of isosceles triangles, the angles at their bases are equal. I.e:

<ОАВ = <ОВА = 67⁰;

Means:

<OBC = <ABC – <OBA = 75⁰ – 67⁰ = 8⁰;

Wherein:

<OBC = <BCO = 8⁰.

Answer: the required angle <ВСО is 8⁰.