Question

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

Explanation:

Step1: Recall the definition of diameter

A diameter is a straight line passing through the center of a circle and connecting two points on the circle. In the given circle, \(\overline{PS}\) is a diameter.

Step2: Recall the definition of radius

A radius is a straight line from the center of a circle to a point on the circle. \(\overline{ON}\), \(\overline{OS}\), \(\overline{OP}\) are radii.

Step3: Recall the definition of chord

A chord is a straight line connecting two points on a circle. \(\overline{QR}\), \(\overline{PS}\) are chords.

Step4: Use the relationship between diameter and radius

The length of a diameter \(d\) and radius \(r\) is given by \(d = 2r\). Given \(d=\overline{PS} = 6\) units. Since \(r=\overline{ON}\) and \(d = 2r\), then \(r=\frac{d}{2}\). Substituting \(d = 6\) into the formula, we get \(r=\frac{6}{2}=3\) units.

Answer:

(a) \(\overline{PS}\)
(b) \(\overline{ON}\) (or \(\overline{OS}\) or \(\overline{OP}\))
(c) \(\overline{QR}\) (or \(\overline{PS}\))
(d) \(3\) units