Question

a circle with center i is shown in the figure below. (a) name a radius: (b) name a diameter: (c) name a chord: (d) if the length of (overline{tv}) is 9 units, what is the length of (overline{qu})?

Explanation:

Step1: Recall the definition of radius

A radius is a line segment from the center of the circle to any point on the circle. So, \( \overline{TV}\) (or \( \overline{TU}\), \( \overline{TQ}\)) is a radius.

Step2: Recall the definition of diameter

A diameter is a line segment passing through the center of the circle with both endpoints on the circle. So, \( \overline{QU}\) (or \( \overline{VX}\)) is a diameter.

Step3: Recall the definition of chord

A chord is a line segment with both endpoints on the circle. So, \( \overline{SR}\) (or \( \overline{QU}\), \( \overline{VX}\), \( \overline{VU}\)) is a chord.

Step4: Use the property of diameter and radius

Since \( \overline{TV}\) is a radius (\(r = 9\) units) and \( \overline{QU}\) is a diameter (\(d=2r\)). Then \(d = 2\times9=18\) units.

Answer:

(a) \( \overline{TV}\) (or \( \overline{TU}\), \( \overline{TQ}\))
(b) \( \overline{QU}\) (or \( \overline{VX}\))
(c) \( \overline{SR}\) (or \( \overline{QU}\), \( \overline{VX}\), \( \overline{VU}\))
(d) \(18\) units