Suppose a line is tangent to a circle at A. Another line through A intersects the circle again at B; if the shorter arc AB is 50∘ of the circle, what is the acute angle between the lines?
The angle between the tangent and the secant is actually equal to the measure of the minor arc subtended by the secant. In this case, the minor arc AB measures 180° - 50° = 130°.
Therefore, the acute angle between the tangent and the secant is 130°/2 = 65°.