Question

a circle with center l is shown in the figure below.
(a) name a radius:
(b) name a diameter:
(c) name a chord:
(d) if the length of \\(\overline{lo}\\) is 8 units, what is the length of \\(\overline{mn}\\)? units

Explanation:

Step1: Recall definitions

• Radius: Segment from center to circle (e.g., \( \overline{LO} \), \( \overline{LM} \), \( \overline{LN} \)).
• Diameter: Chord through center (e.g., \( \overline{MN} \)).
• Chord: Segment with endpoints on circle (e.g., \( \overline{PQ} \), \( \overline{MN} \)).
• Diameter is \( 2 \times \) radius. \( \overline{LO} = 8 \) (radius), so \( \overline{MN} = 2 \times 8 = 16 \).

Part (a)

A radius is a line from center \( L \) to the circle. So \( \overline{LO} \) (or \( \overline{LM} \), \( \overline{LN} \)) works.

Part (b)

A diameter is a chord through \( L \). \( \overline{MN} \) passes through \( L \), so it's a diameter.

Part (c)

A chord has endpoints on the circle. \( \overline{PQ} \) (or \( \overline{MN} \)) works.

Part (d)

\( \overline{LO} \) is radius (\( r = 8 \)). Diameter \( \overline{MN} = 2r = 2 \times 8 = 16 \).

Answer:

(a) \( \overline{LO} \) (or \( \overline{LM} \), \( \overline{LN} \))
(b) \( \overline{MN} \)
(c) \( \overline{PQ} \) (or \( \overline{MN} \))
(d) \( 16 \)