Question

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

Explanation:

To determine the correct statement, recall the definitions: A chord of a circle is a line segment with both endpoints on the circle. A diameter is a special chord that passes through the center (so it also has both endpoints on the circle and intersects the center).

• Analyze each option:
• First option: Chords have one endpoint on circle and one at center? No, chords have two on circle. Eliminate.
• Second option: Both chords (two endpoints on circle) and diameters (two endpoints on circle, and must intersect center as diameters pass through center). This matches definitions.
• Third option: Chords have two on circle, diameters don't have one at center (they have two on circle and pass through center). Eliminate.
• Fourth option: Chords don't need to intersect center (only diameters do). Eliminate.

Answer:

B. Both chords and diameters have two endpoints on a circle. Diameters must intersect the center of a circle. (Assuming the second box is labeled B; if labels are different, adjust, but based on content, the second option's text is correct.)