Question

cle with center o is shown in the figure below.
(a) name a radius:
(b) name a diameter:
(c) name a chord:
(d) if the length of \overline{on} is 6 units,
what is the length of \overline{pq}? 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, $\overline{ON}$ (or $\overline{OP}$, $\overline{OQ}$) 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, $\overline{PQ}$ is a diameter.

Step3: Recall the definition of chord

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

Step4: Calculate the length of diameter

Since the radius $r = \overline{ON}=6$ units and the diameter $d = 2r$. Substitute $r = 6$ into the formula $d = 2r$, we get $d=\overline{PQ}=2\times6$.

Answer:

(a) $\overline{ON}$ (or $\overline{OP}$, $\overline{OQ}$)
(b) $\overline{PQ}$
(c) $\overline{MR}$ (or $\overline{PQ}$)
(d) $12$ units