Question

a circle with center q is shown in the figure below. (a) name a diameter: (b) name a radius: (c) name a chord: (d) if the length of \\( \overline { n r } \\) is 8 units, what is the length of \\( \overline { q s } \\)? 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 \(Q\), \(\overline{NR}\) is a diameter.
• (b) A radius is a line segment from the center of the circle to a point on the circle. So, \(\overline{QS}\) (or \(\overline{QN}\), \(\overline{QR}\)) is a radius.
• (c) A chord is a line segment with both endpoints on the circle. \(\overline{OP}\) (or \(\overline{NR}\)) is a chord.
• (d) The length of the diameter \(\overline{NR}\) is \(8\) units. The radius is half of the diameter. Since \(\overline{QS}\) is a radius and \(QS=\frac{1}{2}NR\), substituting \(NR = 8\) gives \(QS = 4\) units.

Answer:

(a) \(\overline{NR}\)
(b) \(\overline{QS}\) (or \(\overline{QN}\), \(\overline{QR}\))
(c) \(\overline{OP}\) (or \(\overline{NR}\))
(d) \(4\) units