# Ch 12: Explorations in Core Math Geometry Chapter 12: Circles

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Circles chapter of your textbook.
- Watch fun videos that cover the circle concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the geometry topics covered in the textbook chapter, including:

- The parts of a circle, including tangent, chord and arcs
- Finding the area and circumference of circles
- Converting between radians and degrees
- Measuring inscribed angles
- The theorems for circumscribed angles
- The secant-tangent product theorem

*Explorations in Core Math is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Parts of a Circle

After watching this video lesson, you will be able to identify the parts of a circle. You will learn the names of four different parts of a circle along with what each part does for the circle.

### 2. 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.

### 3. Chord of a Circle: Definition & Formula

In this lesson, you'll learn the definition of a chord of a circle. You will also learn the formulas to find the chord of a circle and then look at some examples.

### 4. 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.

### 5. Circles: Area and Circumference

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.

### 6. 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.

### 7. Converting Between Radians and Degrees

Angles can be measured in degrees or radians. This lesson will explore the difference and provide you with a simple calculation that can be used to convert degrees into radians and radians into degrees.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. Circumscribed Angle: Definition & Theorem

Geometry involves many different shapes. In this lesson, we will deal with a circle and two lines tangent to the circle. This forms a circumscribed angle, which we will learn how to identify and how to calculate its angle.

### 12. Secant-Tangent Product Theorem: Definition & Use

In this lesson, we will review secants and tangents of circles. After this, we will look at the secant-tangent product theorem, and use examples to show how to use this theorem in general and in real world applications.

### 13. How to Find the Equation of a Circle

There are two commonly used forms of equations for a circle, in this lesson we'll take a few minutes to examine and understand both forms, and be able to convert from one to the other.

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### Other Chapters

Other chapters within the Explorations in Core Math - Geometry: Online Textbook Help course

- Explorations in Core Math Geometry Chapter 1: Foundations for Geometry
- Explorations in Core Math Geometry Chapter 2: Geometric Reasoning
- Explorations in Core Math Geometry Chapter 3: Parallel and Perpendicular Lines
- Explorations in Core Math Geometry Chapter 4: Triangle Congruence
- Explorations in Core Math Geometry Chapter 5: Properties and Attributes of Triangles
- Explorations in Core Math Geometry Chapter 6: Polygons and Quadrilaterals
- Explorations in Core Math Geometry Chapter 7: Similarity
- Explorations in Core Math Geometry Chapter 8: Right Triangles and Trigonometry
- Explorations in Core Math Geometry Chapter 9: Extending Transformational Geometry
- Explorations in Core Math Geometry Chapter 10: Extending Perimeter, Circumference and Area
- Explorations in Core Math Geometry Chapter 11: Spatial Reasoning
- Explorations in Core Math Geometry Chapter 13: Probablity