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 the radius of the circle. What is the measure of the angle between the tangent and the chord?

Answer 1

The measure of the angle between the tangent and the chord is 90 degrees.

This can be understood by using the property that the radius drawn to the point of tangency is perpendicular to the tangent line. Since the chord is the same length as the radius and connects two points on the circle, it must pass through the point of tangency.

Therefore, the chord is a diameter of the circle and the angle between the tangent and the chord is the angle formed by the diameter and the tangent line. In a circle, the angle between a diameter and a tangent line is always 90 degrees.