Question

a center n is shown in the figure below. (a) name a diameter: (b) name a radius: (c) name a chord: (d) if the length of ko is 4 units, what is the length of np? units

Explanation:

Step1: Recall definitions

• A diameter is a line segment passing through the center with endpoints on the circle. So, $\overline{KO}$ is a diameter.
• A radius is a line segment from the center to a point on the circle. $\overline{NP}$ is a radius.
• A chord is a line segment with endpoints on the circle. $\overline{ML}$ is a chord.

Step2: Use radius - diameter relationship

If the length of diameter $\overline{KO}$ is $d = 4$ units, and the radius $r$ of a circle is related to the diameter by the formula $r=\frac{d}{2}$. Since $\overline{NP}$ is a radius and $\overline{KO}$ is a diameter of the same circle, and all radii of a circle are equal. So, $|\overline{NP}|=\frac{|\overline{KO}|}{2}$.

Answer:

(a) $\overline{KO}$
(b) $\overline{NP}$ (or $\overline{NK},\overline{NO}$)
(c) $\overline{ML}$ (or $\overline{KO},\overline{MP}$)
(d) $2$ units