Question

A tangent to a circle at point A is given, and point A is an endpoint of a chord, which is the same length as radius of the circle. What is the measure of angle between the tangent and the chord?

Answer 1

30°

Explanation:

The angle in question is half the measure of the angle subtended by the chord, which is 60°. The chord is equal to a radius in length, so it and the radii to its ends form an equilateral triangle. The angle at the center of the circle is then 60°.

Half the measure of the subtended angle is 60°/2 = 30°.