Question

a circle with center h is shown in the figure below.
(a) name a diameter:
(b) name a radius:
(c) name a chord:
(d) if the length of \\(\overline{ij}\\) is 6 units, what is the length of \\(\overline{hk}\\)? \\(\square\\) units

Explanation:

Step1: Recall circle definitions

• Diameter: A chord passing through the center. So \( \overline{IJ} \) (since it passes through H).
• Radius: A segment from center to circle. E.g., \( \overline{HJ} \), \( \overline{HI} \), \( \overline{HK} \).
• Chord: A segment with both endpoints on the circle. E.g., \( \overline{LM} \), \( \overline{IJ} \).

Step2: Solve part (d)

• \( \overline{IJ} \) is a diameter (length 6). Radius \( \overline{HK} \) is half the diameter. So \( HK=\frac{IJ}{2}=\frac{6}{2}=3 \).

Answer:

(a) \( \overline{IJ} \)
(b) \( \overline{HJ} \) (or \( \overline{HI} \), \( \overline{HK} \))
(c) \( \overline{LM} \) (or \( \overline{IJ} \))
(d) 3