A tangent is drawn to the circle. A chord is drawn through the tangency point, cutting off an arc of 126º from the circle.

A tangent is drawn to the circle. A chord is drawn through the tangency point, cutting off an arc of 126º from the circle. What is the angle between a chord and a tangent?

The location of the chord drawn from point A is possible in two ways.

The first is when the chord AB is located to the left of the radius OA. The degree measure of the smaller arc AB is 126, then the angle BAC between the chord and the tangent is half the degree measure of the arc AB. Angle BAC = 126/2 = 63.

The second option, the chord AB1 is located to the right of the radius OA. Then the degree measure of the larger arc AB1 = 360 – 126 = 234.

The angle В1АС between the chord and the tangent is equal to half the degree measure of the larger arc AB1. Angle В1АС = 234/2 = 117.

Answer: The angle between the chord and the tangent is 63 or 117.