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 { i j } \\) is 8 units, what is the length of \\( \overline { h k } \\)? units

Explanation:

• (a) A diameter is a line segment passing through the center of the circle with both endpoints on the circle. In the given circle with center \(H\), \(\overline{IJ}\) is a diameter.
• (b) A radius is a line segment from the center of the circle to a point on the circle. \(\overline{HK}\) (or \(\overline{HI}\), \(\overline{HJ}\)) is a radius.
• (c) A chord is a line segment with both endpoints on the circle. \(\overline{KL}\) (or \(\overline{IJ}\), \(\overline{ML}\)) is a chord.
• (d) The length of the diameter \(\overline{IJ}\) is \(8\) units. The radius is half of the diameter. Since \(\overline{HK}\) is a radius, and \(r=\frac{d}{2}\), where \(d = 8\) (length of diameter \(\overline{IJ}\)), then the length of \(\overline{HK}\) is \(\frac{8}{2}=4\) units.

Answer:

(a) \(\overline{IJ}\)
(b) \(\overline{HK}\) (or \(\overline{HI}\), \(\overline{HJ}\))
(c) \(\overline{KL}\) (or \(\overline{IJ}\), \(\overline{ML}\))
(d) \(4\) units