Question

checkpoint: parts of a circle
use the following image to answer the questions below.

1. how many radii do you see?

a. 0 c. 2
b. 1 d. 3

1. what is segment \\(\overline{ge}\\) called?

a. chord c. tangent line
b. secant line d. none of the above

1. in reference to segment \\(\overline{ad}\\), choose all that apply.

a. it is a diameter. d. a and d are points of tangency.
b. \\(2(ad) = ac\\) e. c is the midpoint.
c. it is a chord.

1. how would you classify \\(\overarc{af}\\)?

a. minor arc c. major arc
b. semicircle d. none of the above

1. if c and f were to be connected by a segment, what term would apply?

a. radius c. point of tangency
b. chord d. diameter

1. how many degrees is \\(\overarc{afd}\\)?

Explanation:

Step1: Identify radii in the circle

A radius is a segment from the center (C) to the circle's edge. The radii are $CA$, $CD$. Count: 2.

Step2: Classify segment $\overline{GE}$

$\overline{GE}$ touches the circle at exactly one point (F), so it is a tangent line.

Step3: Analyze segment $\overline{AD}$

• $\overline{AD}$ passes through center C, so it is a diameter.
• A diameter is a type of chord.
• C is the midpoint of $\overline{AD}$ (since $CA=CD$).

Step4: Classify arc $\overset{\frown}{AF}$

$\overset{\frown}{AF}$ is shorter than a semicircle, so it is a minor arc.

Step5: Classify segment $\overline{CF}$

$\overline{CF}$ connects center C to circle edge F, so it is a radius.

Step6: Find measure of $\overset{\frown}{AFD}$

$\overset{\frown}{AFD}$ spans half the circle (from A to D through F), so it is a semicircle with measure $180^\circ$.

Answer:

1. c. 2
2. c. Tangent line
3. a. It is a diameter., c. It is a chord., e. C is the midpoint.
4. a. Minor arc
5. a. Radius
6. $180^\circ$