Question

try again
your answer is incorrect.

• (b): your response for a diameter is incorrect, because there is no segment drawn there.

a circle with center t is shown in the figure below.
(a) name a radius:
(b) name a diameter:
(c) name a chord:
(d) if the length of is 10 units,
what is the length of ?

Explanation:

Step1: Recall the definitions

• Radius: A segment from the center of a circle to a point on the circle.
• Diameter: A segment passing through the center of a circle with both endpoints on the circle.
• Chord: A segment with both endpoints on the circle.

Step2: Analyze each part

• (a) Since \(TS\) is from the center \(T\) to a point \(S\) on the circle, \(TS\) is a radius. Another radius could be \(TU\) or \(TV\).
• (b) A diameter is a segment passing through the center. If \(TV\) and \(TU\) are radii and collinear (assuming the figure is drawn correctly in terms of straight - line through the center), then \(UV\) (if \(U\) and \(V\) are on opposite sides of the center) is a diameter. But since the center is \(T\), and we know that a diameter \(d = 2r\). If \(r=\overline{TS} = 10\) units, and \(\overline{UV}\) (a diameter) has length \(2\times10=20\) units. But looking at the given figure (assuming standard circle - center notation), \(\overline{SV}\) is not a diameter (as per the feedback). A correct diameter could be \(\overline{UV}\) (assuming \(U\) and \(V\) are endpoints of a diameter).
• (c) A chord is a segment with endpoints on the circle. \(\overline{WR}\) is a chord. Another chord could be \(\overline{UV}\) (since it has endpoints \(U\) and \(V\) on the circle)
• (d) Given that \(r = \overline{TS}=10\) units. Since \(\overline{UV}\) is a diameter (if \(U\) and \(V\) are endpoints of a diameter), and the formula for the length of a diameter \(d\) in terms of the radius \(r\) is \(d = 2r\). Substituting \(r = 10\) units, we get \(d=\overline{UV}=2\times10 = 20\) units.

Answer:

(a) \(\overline{TS}\) (or \(\overline{TU}\) or \(\overline{TV}\))
(b) \(\overline{UV}\)
(c) \(\overline{WR}\) (or \(\overline{UV}\))
(d) \(20\) units