Question

(a) name a diameter:
(b) name a radius:
(c) name a chord:
(d) if the length of $overline{kl}$ is 6 units,
what is the length of $overline{jm}$? $square$ units

Explanation:

Part (a)

Step1: Recall diameter definition

A diameter is a chord passing through the center, connecting two points on the circle. Assume the circle has center (say) \( M \), and points \( J, K, L \) on it. If \( \overline{JM}L \) (wait, better: a diameter is a line segment through center, endpoints on circle. So if \( \overline{JL} \) passes through center \( M \), then \( \overline{JL} \) is a diameter. (Assuming standard circle with center \( M \), \( K \) on circle, \( \overline{KL} \) maybe radius? Wait, part (d) says \( \overline{KL} = 6 \), \( \overline{JM} \) length. Let's infer:

Step1: Define diameter

Diameter: chord through center, endpoints on circle. So if center is \( M \), and \( J, L \) are on circle with \( M \) between them, then \( \overline{JL} \) is diameter.

Step1: Recall radius definition

Radius: segment from center to circle. If center is \( M \), and \( K \) is on circle, then \( \overline{MK} \) (or \( \overline{MJ} \), \( \overline{ML} \)) is radius. Given \( \overline{KL} = 6 \), maybe \( \overline{MK} \) is radius (since \( K \) and \( L \)? Wait, no—if \( \overline{KL} \) is 6, and \( M \) is center, then \( \overline{MK} \) and \( \overline{ML} \) are radii, so \( \overline{MK} = \overline{ML} = r \), and \( \overline{KL} \) is a chord? Wait, no—part (d) says \( \overline{KL} = 6 \), find \( \overline{JM} \). So \( \overline{JM} \) is radius? Wait, maybe \( J, M, L \) are colinear, \( M \) is center, so \( \overline{JM} \) is radius, \( \overline{JL} \) is diameter. Then \( \overline{KL} \) is a chord, but if \( \overline{KL} = 6 \), and \( M \) is center, maybe \( \overline{KL} \) is a radius? No, radius is from center to circle. Wait, maybe \( K \) is on circle, \( M \) is center, so \( \overline{MK} \) is radius.

Step1: Define radius

Radius: center to circle. So \( \overline{MK} \) (or \( \overline{MJ} \), \( \overline{ML} \)) is radius.

Step1: Recall chord definition

Chord: segment with both endpoints on circle. So \( \overline{KL} \) (if \( K, L \) are on circle) or \( \overline{JL} \) (diameter is a chord), or \( \overline{JK} \) (if \( J, K \) are on circle). Given \( \overline{KL} = 6 \), so \( \overline{KL} \) is a chord.

Step1: Define chord

Chord: endpoints on circle. So \( \overline{KL} \) is a chord.

Answer:

\(\overline{JL}\) (or other valid diameter, depends on diagram; assuming standard, \( \overline{JL} \) as diameter)

Part (b)