Angles and Intercepted Arcs

In this lesson, we will learn some formulas relating the angles and the intercepted arcs of circles.

• Measure of a central angle.
• Measure of an inscribed angle - angle with its vertex on the circle
• Measure of an angle with vertex inside a circle.
• Measure of an angle with vertex outside a circle.

Central Angle

A central angle is an angle with its vertex is at the center of the circle. The measure of a central angle is equal to the measure the intercepted arc.

The formula is

Central angle = intercepted arc

Example:

Find the value of x

Solution:

Inscribed Angle - Angle with its vertex on the circle

An inscribed angle is an angle with its vertex on the circle. The meaure of an inscribed angle is half the measure the intercepted arc.

The formula is

Inscribed angle = (intercepted arc)

Example:

Find the value of x

Solution:

The following video shows how to apply the formula for inscribed circles.

Angle with vertex inside the circle

The measure of an angle with its vertex inside the circle is half the sum of the intercepted arcs.

The formula is

Angle = (sum of intercepted arcs)

Example:

Find the value of x

Solution:

The following video shows how to apply the formula for angles with vertex inside the circle.

Angle with vertex outside the circle

The measure of an angle with its vertex outside the circle is half the difference of the intercepted arcs.

The formula is

Angle = (difference of intercepted arcs)

Example:

Find the value of x

The following video shows how to apply the formula for angles with vertex outside circle

.

Custom Search

© Copyright 2005, 2012 - onlinemathlearning.com
Embedded content, if any, are copyrights of their respective owners.