Angles and Arcs in Circles

Angles and Arcs in Circles

Objectives

• Identify central angles, minor arcs, major arcs, semicircles and find their measures

• Find arc lengths

Multiple Choice

Which of the following best represents line GH?

• tangent

• chord

• segment

• secant

Multiple Choice

Which of the following best represents line BK?

• tangent

• chord

• segment

• secant

Multiple Select

Which of the following best represents the point of tangency in circle J?

• A

• E

• K

• G

What is a Central Angle?

A central angle is an angle whose vertex is at the center of the circle and is formed by two radii.

Ways to label angles

• By the Vertex: $\angle O$   

• By the points:  $\angle AOB$        (Vertex should always be in the middle of two points)

• If angles are numbers then can be labeled by number.           Example:  $\angle1$  

Multiple Select

Choose the correct way(s) to label the angle.

• $\angle ABC$

• $\angle CBA$

• $\angle B$

• $\angle C$

Ways of Labeling Arcs

• Use the endpoints of the arc:

• CB or BC would be the blue arc

• CDB or BDC would be the red arc (use points in-between endpoints to indicate which direction to go in)

• Arc CBD (Start at C, go to B then go to D)

Multiple Select

Correctly choose the correct names for the central angle and its intercepted arc

• $\angle CDA$ ; Arc BD

• $\angle FEB$ ; Arc BCF

• $\angle CAD$ ; Arc CFD

• $\angle CFE$ ; Arc BED

Multiple Select

Choose the correct way to label the pink arc

• CB

• CAB

• AB

• BAC

• CDB

Labeling arcs and angles

• Labeling angles stays the same as before

• Labeling the arc stays the same

• The intercepted arc corresponds to the endpoints of the angle. Example: The intercepted arc of  $\angle EDG$  is Arc GE

Multiple Select

Check the boxes that have the correct label for the red arc.

• CDB

• CB

• D

• CAB

• BDC

Labeling Inscribed Angles and Arcs

Labeling Inscribed Angles is the same as normal angles
Labeling Arcs is the same.
Example: the inscribed angle is  $\angle EFG$  and the intercepted arc would be the endpoints of the angle EG

Multiple Select

Correctly choose the correct names for the inscribed angle and its intercepted arc

• $\angle CDA$ ; Arc BD

• $\angle FEB$ ; Arc BFD

• $\angle CAD$ ; Arc CFD

• $\angle CFE$ ; Arc BED