Question

activity 1: know my terms and conditions... use the figure below to identify and name the following terms related to ⊙a. then, answer the questions that follow. 1. a radius 2. a diameter 3. a chord 4. a semicircle 5. a minor arc 6. a major arc 7. 2 central angles 8. 2 inscribed angles

Explanation:

Step1: Define radius

A radius is a line - segment from the center of a circle to a point on the circle. In circle A, $\overline{AE}$, $\overline{AJ}$, $\overline{AN}$ are radii.

Step2: Define diameter

A diameter is a chord that passes through the center of the circle. In circle A, $\overline{JN}$ is a diameter (since it passes through A).

Step3: Define chord

A chord is a line - segment whose endpoints lie on the circle. $\overline{LN}$, $\overline{JN}$, $\overline{LE}$, etc. are chords.

Step4: Define semicircle

A semicircle is an arc that is half of a circle. For example, arc $\overset{\frown}{JEN}$ or arc $\overset{\frown}{JLN}$ are semicircles.

Step5: Define minor arc

A minor arc is an arc that is less than a semicircle. For example, arc $\overset{\frown}{LE}$, arc $\overset{\frown}{EN}$ are minor arcs.

Step6: Define major arc

A major arc is an arc that is greater than a semicircle. For example, arc $\overset{\frown}{LJN}$ (excluding the minor part between L and N) is a major arc.

Step7: Define central angle

A central angle is an angle whose vertex is the center of the circle. $\angle JAN$, $\angle EAN$ are central angles.

Step8: Define inscribed angle

An inscribed angle is an angle whose vertex lies on the circle and whose sides are chords of the circle. $\angle JLN$, $\angle JEN$ are inscribed angles.

Answer:

1. $\overline{AE}$, $\overline{AJ}$, $\overline{AN}$
2. $\overline{JN}$
3. $\overline{LN}$, $\overline{JN}$, $\overline{LE}$ (any chord)
4. arc $\overset{\frown}{JEN}$, arc $\overset{\frown}{JLN}$
5. arc $\overset{\frown}{LE}$, arc $\overset{\frown}{EN}$ (any minor arc)
6. arc $\overset{\frown}{LJN}$ (any major arc)
7. $\angle JAN$, $\angle EAN$
8. $\angle JLN$, $\angle JEN$