About This Chapter
Circular Arc & Circles in Coordinate Geometry - Chapter Summary
Our short lessons introduce you to circles, circular arcs, their definitions and examples of both. You'll learn how to find the measure of an inscribed angle and discover what some of the theorems that govern circles and tangents look like. Lessons discuss inscribed and circumscribed figures, arc lengths and the chord theorems of circles. After you review this chapter, you will be able to:
- Differentiate between central and inscribed angles
- Find the measure of an arc and complete the square
- Measure angles and lengths involving secants, chords and tangents
- Understand what completing the square has to do with business decisions
- Graph circles and identify them just by looking at their formula
Our video lessons are short and professionally created, so studying is simple. Printable transcripts help you focus on the most important topics and vocabulary words for handy offline review. If you need assistance with any of the lessons or topics, contact one of our instructors for help. These learning materials work together like a comprehensive online study guide you can access from anywhere at any time.
1. Circular Arcs and Circles: Definitions and Examples
What is a circle? In this lesson, find out all about the circle and its many parts, including circular arcs and semicircles. Also, discover how a locus works in creating a circle, parallel lines and more.
2. Central and Inscribed Angles: Definitions and Examples
When we're working with circles, there are two key angles to know: central angles and inscribed angles. These angles have a few special theorems, which we'll discuss and practice using in this lesson.
3. Measure of an Arc: Process & Practice
What is the measure of an arc? And what is the difference between a minor arc and a major arc? Find out all that and practice finding the measure of an arc in this lesson.
4. How to Find the Measure of an Inscribed Angle
Finding the measure of an inscribed angle requires knowing a little information. In this lesson, we'll find the measure of an inscribed angle when we know the measure of the central angle or one or more of the arcs formed by the angle.
5. Tangent of a Circle: Definition & Theorems
What happens when a line just barely touches a circle? It's a tangent! In this lesson, we'll learn all about tangents to circles, including a few key theorems. We'll also look at tangent circles.
6. Measurements of Angles Involving Tangents, Chords & Secants
When lines and circles meet, angles are formed. Fortunately, we can determine the measure of these angles, whether they're formed by tangents, secants or chords, just by knowing the measure of the created arcs.
7. Measurements of Lengths Involving Tangents, Chords and Secants
The lengths of chords, tangents and secants take on unique relationships when they're drawn on circles. In this lesson, we'll define those relationships and see them in action.
8. Inscribed and Circumscribed Figures: Definition & Construction
A square and a circle may be different shapes, but they still can have a unique relationship. In this lesson, we'll learn about inscribed and circumscribed figures.
9. Arc Length of a Sector: Definition and Area
In this lesson, we'll slice up a circle like it's a pizza and learn how to find out useful information about our slices. We'll find out the area of these sectors, or pie slices. We'll also learn about arc lengths.
10. How to Complete the Square
Completing the square can help you learn where the maximum or minimum of a parabola is. If you're running a business and trying to make some money, it might be a good idea to know how to do this! Find out what I'm talking about here.
11. Graphing Circles: Identifying the Formula, Center and Radius
Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.
12. Chord Theorems of Circles in Geometry
Watch this video lesson to learn how a radius will always bisect a perpendicular chord and how equidistant chords will always be congruent to each other. Also, see an example of how you can use these two theorems.
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