A chord AB is drawn in a circle centered at point O. The angle between chord AB and the tangent to the circle passing

A chord AB is drawn in a circle centered at point O. The angle between chord AB and the tangent to the circle passing through point B is 55 degrees. Find the degree measure of the central angle AOB.

By the property of the tangent to the circle, the radius drawn to the point of tangency is perpendicular to the tangent, then the angle OBC = 90.

OBA angle = (OBC – ABC) = (90 – 55) = 35

The AOB triangle is isosceles, since ОА = ОВ = R, then the angle ОАВ = ОВА = 35.

Angle AOB = (180 – OAB – OBA) = (180 – 35 – 35) = 110.

Answer: The central angle of the AOB is 110.