Question

which statements are correct? choose four correct answers. a radius is always congruent to another radius of the same circle. a chord can be longer than a diameter of the same circle. a chord can be shorter than a radius of the same circle. a diameter is always a chord. a chord is sometimes a radius. a tangent is never a secant.

Explanation:

1. In a circle, all radii have the same length, so a radius is always congruent to another radius of the same circle.
2. A chord is a line - segment connecting two points on the circle. A diameter is the longest chord in a circle, but other chords can be shorter than the diameter.
3. A chord can be shorter than a radius. For example, a very short chord close to a single point on the circle.
4. A diameter is a special chord that passes through the center of the circle, so a diameter is always a chord.
5. A chord is a line - segment within the circle connecting two points on the circle, while a radius connects the center to a point on the circle, so a chord is never a radius.
6. A tangent is a line that touches the circle at exactly one point, and a secant is a line that intersects the circle at two points. So a tangent is never a secant.

Answer:

A. A radius is always congruent to another radius of the same circle.
B. A chord can be longer than a diameter of the same circle.
C. A chord can be shorter than a radius of the same circle.
D. A diameter is always a chord.
E. A tangent is never a secant. (Choose any four of the above - correct statements as required by the question)