Question

a circle with center j is shown in the figure below. (a) name a diameter: (b) name a radius: (c) name a chord: (d) if the length of \\(\overline{kl}\\) is 10 units, what is the length of \\(\overline{ji}\\)? units

Explanation:

Step1: Recall definitions

• Diameter: A chord passing through the center.
• Radius: A segment from center to circle.
• Chord: A segment with both endpoints on the circle.
• Radius is half the diameter.

Step2: Solve (a)

A diameter passes through center \( J \). \( \overline{KL} \) passes through \( J \), so it's a diameter.

Step3: Solve (b)

A radius is from \( J \) to the circle. \( \overline{JI} \) (or \( \overline{JK} \), \( \overline{JL} \)) is a radius.

Step4: Solve (c)

A chord has endpoints on the circle. \( \overline{HM} \) (or \( \overline{KL} \)) is a chord.

Step5: Solve (d)

\( \overline{KL} \) is diameter (\( 10 \) units). Radius \( \overline{JI} = \frac{1}{2} \times \) diameter \( = \frac{10}{2} = 5 \).

Answer:

(a) \( \overline{KL} \)
(b) \( \overline{JI} \) (or \( \overline{JK} \), \( \overline{JL} \))
(c) \( \overline{HM} \) (or \( \overline{KL} \))
(d) \( 5 \)