Question

geometry, measurement, data analysis
introduction to a circle: diameter, radius, and chord
circle with center r is shown in the figure below.
(a) name a diameter:
(b) name a radius:
(c) name a chord:
(d) if the length of (overline{sv}) is 10 units,
what is the length of (overline{rq})? units

Explanation:

Step1: Recall definitions

A diameter is a line segment passing through the center with endpoints on the circle. A radius is a line segment from the center to a point on the circle. A chord is a line segment with endpoints on the circle.

Step2: Name diameter

For part (a), \(\overline{SV}\) is a diameter as it passes through center \(R\) and has endpoints \(S\) and \(V\) on the circle.

Step3: Name radius

For part (b), \(\overline{RQ}\) (or \(\overline{RS}\), \(\overline{RV}\)) is a radius as it goes from center \(R\) to a point (\(Q\), \(S\), or \(V\)) on the circle.

Step4: Name chord

For part (c), \(\overline{TU}\) (or \(\overline{SV}\)) is a chord. \(\overline{SV}\) is also a diameter (a special - case chord).

Step5: Calculate radius length

For part (d), if the length of diameter \(\overline{SV}=10\) units, and the radius \(r=\frac{d}{2}\) (where \(d\) is the diameter). So, if \(d = \overline{SV}=10\) units, then \(r=\overline{RQ}=\frac{10}{2}=5\) units.

Answer:

(a) \(\overline{SV}\)
(b) \(\overline{RQ}\) (or \(\overline{RS}\), \(\overline{RV}\))
(c) \(\overline{TU}\) (or \(\overline{SV}\))
(d) \(5\) units