AC and EB are diameters of circle O. Identify each arc as a major arc, minor arc or a semicircle of the circle. Then find its measure.

1. m$\widetilde{EA}$ 2. m$\widetilde{CBD}$ 3. m$\widetilde{DC}$ 4. m$\widetilde{DEB}$

5. m$\widetilde{AB}$ 6. m$\widetilde{CDA}$

1. $\widetilde{EA}$

The end points of the arc are E and A

Measure of the central angle = m ∠EOA = m ∠BOC = 57º. Vertical angles are congruent.

Since the measure of the central angle is less than 180º, the arc is a minor arc.

$\widetilde{EA}$ is a

** minor arc** and m$\widetilde{EA}$ =

**57º.**2. $\widetilde{CBD}$

The end points of the arc are C and D.

Measure of the central angle = m ∠COD = 95º

The point B is not inside the angle COD. Hence $\widetilde{CBD}$ is a

**major arc**.

m$\widetilde{CBD}$ = 360 - 95 =

**265º**.

3. $\widetilde{DC}$

The end points of the arc are C and D.

Measure of the central angle = m ∠COD = 95º

$\widetilde{DC}$ is a

**minor arc**.

m$\widetilde{DC}$ =

**95º**.

4. $\widetilde{DEB}$

The end points of the arc are D and B.

Measure of the central angle = m ∠DOB = 95 + 57 = 152º.

The point E is not inside the angle DOB. Hence $\widetilde{DEB}$ is a

**major arc**.

m$\widetilde{DEB}$ = 360 - 152 =

**208º**.

5. $\widetilde{AB}$

The end points of the arc are A and B.

Measure of the central angle = ∠AOB = ∠EOC = 28 + 95 = 123º. Vertical angles are congruent.

$\widetilde{AB}$ is a

**minor arc**.

m$\widetilde{AB}$ =

**123º**.

6. $\widetilde{CDA}$

The end points of the arc are C and A.

Measure of central angle = m ∠ COA = 180º AC is a diameter of the circle.

$\widetilde{CDA}$ is a

**semicircle**.

m$\widetilde{CDA}$ =

**180º**.