The chord AB subtracts the 6 ° arc of a circle. Find the acute angle ABC between this chord

The chord AB subtracts the 6 ° arc of a circle. Find the acute angle ABC between this chord and the tangent to the circle drawn through point B.

Let’s construct the radii of the circle OA and OB. Since the chord AB contracts the arc at 60, the central angle AOB is also equal to 60.

Triangle AOB is isosceles, since OA and OB are circular radii, then the angle OAB = OBA.

Angle ОАВ = ОВА = (180 – AOB) / 2 = (180 – 6) / 2 = 174/2 = 870.

Tangent SV and radius OB are perpendicular to the tangent property.

Then the angle CBO = 90, and the angle ABO = CBO – ABO = 90 – 87 = 3.

Answer: The angle between the chord and the tangent is 3.