In a circle centered at point O from point A of the circle, two chords are drawn, intersecting

In a circle centered at point O from point A of the circle, two chords are drawn, intersecting it at points B and C. What is the angle CAB if the angle CBO = 55 °.

Let’s draw the radii of the circle OB and OС.

The ВOС triangle is isosceles, since OB = OС= R, then the angle OСВ = OBC = 400, then the ВOС angle = (180 – 40 – 40) = 100.

The central angle of the ВOC is based on the BC arc, then the degree measure of the arc is 100.

The inscribed angle BAC rests on the arc BC, then the angle BAC = 100/2 = 50.

Answer: The angle of BAC is 50.