Arc Of A Circle (Simply Explained W/ 8 Examples!) - Calcworkshop

In this geometry lesson, you’re going to learn about the arcs of a circle.

Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)

You’re going to discover how to distinguish between major and minor arcs.

Learn how to use a new addition postulate to find missing measurements, and much more.

So let’s get started!

An arc is a smooth curve joining two points.

Consequently, on a circle, every pair of distinct points determines two arcs:

1. Major Arcs
2. Minor Arcs

This means that a circle can be divided into smaller pieces, where each piece is called an arc.

Minor vs. Major Arcs

What is so amazing about arcs of a circle is that an arc is named according to its angle. A minor arc is less than 180° and is equal to the central angle. The central angle is formed with its vertex at the center of the circle, whereas a major arc is greater than 180°.

In other words, the minor arc is small while the major arc is large. And to reinforce this idea, we use two letters when describing a minor arc and three letters when identifying a major arc.

Major vs. Minor Arc

Arc Addition Postulate

Furthermore, if we know that a circle is 360°, and a circle is divided into one major and one minor arc. Then the sum of the major arc and the minor arc is also 360°. This is called the Arc Addition Postulate.

Arc Addition Postulate Example

Additionally, a particular arc, formed by the diameter of a circle, has the measure of 180° and is called a semicircle, as ck-12 accurately states.

In the video below, you will learn:

1. How to find the measure of central angles, minor arcs, and major arcs.
2. Use the arc addition postulate to find the sum of multiple arcs.
3. Determine if two arcs are congruent.

Video – Lesson & Examples

47 min

• Introduction
• 00:00:22 – Overview of Minor and Major Arcs and the Arc Addition Postulate
• Exclusive Content for Member’s Only

• 00:08:02 – Find the missing measurement for each problem (Examples #1-3)
• 00:28:43 – Overview of congruent arcs (Examples #4-6)
• 00:36:39 – Complete the two-column proof given arcs of a circle (Examples #7-8)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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