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

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

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)

Labeling arcs and angles

Labeling Inscribed Angles and Arcs

Today we are going to learn about the following:

• Central Angle

• Inscribed Angle

• Interior Angle

• Exterior Angle

Central Angle

• A central angle of a circle has a vertex at the center and is formed by two radii.

• The measure of the central angle is the same as the measure of its corresponding arc of the circle.

Inscribed Angle

• An inscribed angle in a circle has a vertex on the circle and is formed by two chords.

• The measure of an inscribed angle is half the measure of its corresponding arc of the circle.

Exterior Angle

Interior Angle

• An interior angle has a vertex inside the circle and is formed by two intersecting chords/secants.

• The measure of an interior angle is half the sum of its corresponding arcs.

• (arc1 + arc2)/2