The chord AB subtracts a circular arc of 112 degrees. Find the angle between this chord

The chord AB subtracts a circular arc of 112 degrees. Find the angle between this chord and the tangent to the circle drawn through point B.

From the center of the circle, point O, draw a radius to the point of tangency B.

By the property of the tangent, the radius of the OB is perpendicular to the tangent of the BC, then the angle OBC = 90.

The AOB triangle is isosceles, since OB = OA = R, then the angle OAB = OBA = (180 – AOB) / 2 = (180 – 112) / 2 = 34.

Angle ABC = OBC – OBA = 90 – 34 = 56.

Answer: The angle between the chord and the tangent is 56.