Question

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

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: Identify diameter

$\overline{HI}$ passes through center $G$ and has endpoints $H$ and $I$ on the circle.

Step3: Identify radius

$\overline{GF}$ (or $\overline{GH}$, $\overline{GI}$) is from center $G$ to a point ($F$, $H$, or $I$) on the circle.

Step4: Identify chord

$\overline{IJ}$ (or $\overline{HI}$, $\overline{IJ}$ is a chord as it has endpoints $I$ and $J$ on the circle; $\overline{HI}$ is also a chord (and a diameter)).

Step5: Calculate radius length

Since $\overline{HI}$ is a diameter of length $4$ units, and radius $r=\frac{d}{2}$ (where $d$ is diameter). So for radius $\overline{GF}$, length is $\frac{4}{2}=2$ units.

Answer:

(a) $\overline{HI}$
(b) $\overline{GF}$ (or $\overline{GH}$, $\overline{GI}$)
(c) $\overline{IJ}$ (or $\overline{HI}$)
(d) $2$ units