Question

a circle 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 hk is 10 units, what is the length of gf? units

Explanation:

Step1: Identify diameter (through center)

A diameter is a chord passing through the center. $\overline{HK}$ passes through $G$, so it is a diameter.

Step2: Identify radius (center to circle edge)

A radius connects the center $G$ to a point on the circle. $\overline{GF}$ is one such segment.

Step3: Identify chord (two circle edge points)

A chord connects two points on the circle. $\overline{JI}$ connects $J$ and $I$ on the circle.

Step4: Relate diameter to radius

Radius is half the diameter. $\overline{GF}$ is a radius, $\overline{HK}$ is a diameter.
$\text{Length of } \overline{GF} = \frac{1}{2} \times \text{Length of } \overline{HK} = \frac{1}{2} \times 10$

Answer:

(a) $\overline{HK}$
(b) $\overline{GF}$
(c) $\overline{JI}$
(d) 5 units