The angle between the tangent and the chord drawn from the tangent point is 37 °.

The angle between the tangent and the chord drawn from the tangent point is 37 °. Find the size of the arc that this chord carves into the circle.

From the center of the circle, point O, draw the radii OB and OS to the ends of the chord AB.

Since OA is the radius to the point of tangency, it is perpendicular to the tangent AC.

Then the angle ОАВ = (ОАС – ВАО) = (90 – 37) = 53.

The AOB triangle is equilateral, since ОА = ОВ = R, and then the angle ОАВ = ОВА = 53.

Then the angle ABO = (180 – ОАВ – ОВА) = (180 – 53 – 53) = 74.

The central angle AOB rests on the arc AB, the degree measure of which is equal to this angle. Arc AB = 74.

Answer: Arc AB is equal to 74.