Question

which is true regarding chords and diameters of circles?
both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.
both chords and diameters have two endpoints on a circle. chords must intersect the center of a circle.
chords have two endpoints on a circle. diameters have one endpoint on a circle and one at the center.
chords have one endpoint on a circle and one at the center. diameters have two endpoints on a circle.

Explanation:

A chord of a circle is defined as a line segment with both endpoints on the circle. A diameter is a special type of chord that must pass through the center of the circle, while regular chords do not need to intersect the center. We evaluate each option against these definitions:

1. The first option matches the definitions of both chords and diameters.
2. The second option is incorrect because chords do not need to intersect the center.
3. The third option is incorrect because diameters have two endpoints on the circle, not one.
4. The fourth option is incorrect because chords have two endpoints on the circle, not one.

Answer:

A. Both chords and diameters have two endpoints on a circle. Diameters must intersect the center of a circle.