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 the circle to a point on the circle. In circle A, $\overline{AJ}$, $\overline{AN}$, $\overline{AE}$, $\overline{AL}$ are radii.

Step2: Define diameter

A diameter is a chord that passes through the center of the circle. In circle A, if we connect two points on the circle through the center, for example, if we consider the line - segment with endpoints on the circle passing through A, there is no such line - segment shown explicitly in the given figure. But if we assume we can draw one, it would be a line like $\overline{LN}$ (if it passed through A).

Step3: Define chord

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

Step4: Define semicircle

A semicircle is an arc of a circle whose endpoints are the endpoints of a diameter. Since no diameter is clearly shown, we can't name a proper semicircle. But if we assume a diameter, say if $\overline{LN}$ was a diameter passing through A, then the two semi - circles would be the two arcs formed by L and N.

Step5: Define minor arc

A minor arc is an arc of a circle that is less than a semicircle. For example, $\overset{\frown}{JE}$, $\overset{\frown}{LE}$, $\overset{\frown}{JN}$, $\overset{\frown}{LN}$ (if it is less than a semi - circle) are minor arcs.

Step6: Define major arc

A major arc is an arc of a circle that is greater than a semicircle. For example, if $\overset{\frown}{JE}$ is a minor arc, then the arc that goes from J to E through the rest of the circle is a major arc. We can name it as $\overset{\frown}{JLE}$ or $\overset{\frown}{JNE}$.

Step7: Define central angle

A central angle is an angle whose vertex is the center of the circle. $\angle JAN$, $\angle EAL$ 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. $\angle JLN$, $\angle ENL$ are inscribed angles.

Answer:

1. $\overline{AJ}$, $\overline{AN}$, $\overline{AE}$, $\overline{AL}$
2. No clear diameter shown (assume $\overline{LN}$ if it passed through A)
3. $\overline{LN}$, $\overline{JE}$, $\overline{LE}$, $\overline{JN}$
4. No clear semicircle shown (assume based on a diameter like $\overline{LN}$)
5. $\overset{\frown}{JE}$, $\overset{\frown}{LE}$, $\overset{\frown}{JN}$, $\overset{\frown}{LN}$ (if less than semi - circle)
6. For example, $\overset{\frown}{JLE}$, $\overset{\frown}{JNE}$
7. $\angle JAN$, $\angle EAL$
8. $\angle JLN$, $\angle ENL$