Question

a arde with center l is shown in the figure below. (a) name a radius: (b) name a diameter: (c) name a chord: (d) if the length of \\( \overline { l n } \\) is 4 units, what is the length of \\( \overline { i m } \\) ? units

Explanation:

Step1: Recall the definition of radius

A radius is a line segment from the center of the circle to a point on the circle. So, \(\overline{LN}\), \(\overline{LM}\), or \(\overline{LI}\) can be 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, \(\overline{MI}\) is a diameter.

Step3: Recall the definition of chord

A chord is a line segment with both endpoints on the circle. So, \(\overline{KJ}\), \(\overline{MI}\), or \(\overline{LN}\) (but \(\overline{LN}\) is also a radius) can be a chord. Let's choose \(\overline{KJ}\).

Step4: Calculate the length of the diameter

If the length of \(\overline{LN}\) (a radius) is \(r = 4\) units, and the diameter \(d\) of a circle is related to the radius by the formula \(d=2r\). Substituting \(r = 4\) into the formula, we get \(d = 2\times4=8\) units.

Answer:

(a) \(\overline{LN}\) (or \(\overline{LM}\), \(\overline{LI}\))
(b) \(\overline{MI}\)
(c) \(\overline{KJ}\) (or \(\overline{MI}\))
(d) \(8\) units