The angle between the chord AB and the tangent BC to the circle is 46.

The angle between the chord AB and the tangent BC to the circle is 46. Find the value of the smaller arc contracted by the chord AB.

From the point O of the circle, draw the radii of the circle to the edges A and B of the chord.

Then the triangle AOB is equilateral, since OA = OB = R, and then the angle ABO = BAO.

By the property of the tangent to the circle, the angle between the tangent and the radius drawn to the tangent point of the straight line, the OBC angle = 900.

Then the angle OBA = OBC – ABC = 90 – 46 = 44.

Central angle AOB = 180 – OAB – OBA = 180 – 44 – 44 = 92.

The degree measure of an arc is equal to the value of the central angle that rests on this arc.

Arc AB = 92.

Answer: The degree measure of the arc AB is equal to 92.