Question

a circle with center j is shown in the figure below. (a) name a radius: (b) name a diameter: (c) name a chord: (d) if the length of \overline{ji} is 7 units, what is the length of \overline{kn}? 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, $\overline{JI}$ (or $\overline{JK}$ or $\overline{JN}$) 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, $\overline{KN}$ is a diameter.

Step3: Recall the definition of chord

A chord is a line segment with both endpoints on the circle. So, $\overline{LM}$ (or $\overline{KN}$) is a chord.

Step4: Calculate the length of the diameter

Since the length of the radius $\overline{JI}$ is 7 units, and the diameter is twice the radius. Using the formula $d = 2r$, where $r = 7$. So, $d=2\times7$.

Answer:

(a) $\overline{JI}$ (or $\overline{JK}$ or $\overline{JN}$)
(b) $\overline{KN}$
(c) $\overline{LM}$ (or $\overline{KN}$)
(d) 14 units