# Ch 9: High School Geometry: Circular Arcs and Circles

### About This Chapter

## Circular Arcs and Circles - Chapter Summary and Learning Objectives

What are the differences between circles and circular arcs? You can discover how to define and illustrate them in this chapter. Meet the measurement methods for arcs, inscribed angles, angles formed by tangents and the distance from a point to a circle. You can also get comfortable with discussing the relationships between circumscribed and inscribed figures. This chapter is designed to teach you:

- Locus of points in circles
- Central and inscribed angles
- Measurement of arcs and inscribed angles
- Construction of tangents to circles
- Inscribed and circumscribed figures
- Identification of regular polygons
- Formulas for circumference and area of circles
- Sector of a circle
- Arc length

Video | Objective |
---|---|

Circular Arcs and Circles Defined | Defines and illustrates a circle as well as terms related to it, such as circular arcs and semicircles. Defines locus of points. Explains how to measure the distance from a point to a circle. |

Central and Inscribed Angles | Defines central and inscribed angles. |

Measure of an Arc | Demonstrates how to measure an arc. |

Measure of an Inscribed Angle | Shows how to determine the measure of an inscribed angle. |

Tangent of a Circle | Defines the tangent of a circle. Discusses postulates about tangents. Constructs a tangent to a circle. Explores situations when there are two circles tangent to each other. |

Measurements of Tangents, Angles, and Segments | Explains how to find measures of angles formed by tangents and lengths of segments involving tangents. |

Inscribed and Circumscribed Figures | Defines inscribed and circumscribed figures. Discusses the relationships involving inscribed and circumscribed figures. Explains how to construct inscribed and circumscribed figures. |

Regular Polygons | Defines and illustrates a regular polygon. Explains how to identify regular polygons and their parts. |

Circles: Area and Circumference | Learn and apply the formulas for area and circumference of circles |

Arc Length of a Sector: Definition and Area | Defines a sector of a circle. Explains how to find the area of a sector. Defines arc length. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. Constructing Inscribed & Circumscribed Triangles

View this lesson to learn how you can construct inscribed and circumscribed triangles. Learn how both involve circles. All you need are a ruler and a compass.

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### Other Chapters

Other chapters within the Geometry: High School course

- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- High School Geometry: Introduction to Geometric Figures
- High School Geometry: Properties of Triangles
- High School Geometry: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Conic Sections
- High School Geometry: Geometric Solids
- High School Geometry: Analytical Geometry
- High School Geometry: Probability
- High School Geometry: Introduction to Trigonometry