# Ch 16: Honors Geometry: Circular Arcs & Circles

### About This Chapter

## Honors Geometry: Circular Arcs & Circles- Chapter Summary

In this chapter we will look at concepts within circular arcs and circles. If you are looking for an alternative to your geometry book, this chapter can help you replace several concepts that are found in your book. Lessons will cover topics that include:

- The properties of circles
- How to find the tangent of a circle
- Finding the area of the arc length
- Measuring an inscribed angle

Lesson | Objective |
---|---|

Properties of Shapes: Circles | Examine the different parts of a circle. |

Circles: Area and Circumference | Know how to calculate the area and circumference of a circle. |

Circular Arcs and Circles: Definitions and Examples | Discover the differences between a semicircle and a circle. |

Measure of an Arc: Process & Practice | Review how to measure an arc of a circle. |

How to Find the Measure of an Inscribed Angle | Find out how to measure an inscribed angle when knowing the central angle or other arc angles. |

How to Construct a Tangent of a Circle | Discover what a tangent is and the theorems surrounding tangents. |

Arc Length of a Sector: Definition and Area | Find out how to determine areas of sectors and arc lengths. |

How to Find the Equation of a Circle | Apply knowledge of circles to different equations. |

Graphing Circles: Identifying the Formula, Center and Radius | Learn about how to graph circles with information such as the center and radius. |

How to Complete the Square | Explore how to complete a square and where the maximum or minimum of a parabola is. |

Completing the Square Practice Problems | Simplify the process of completing a square. |

### 1. Properties of Shapes: Circles

Circles are fundamental to everything we do. But, did you know they're much more than just round shapes? In this lesson, we'll look at the various parts of circles and how they all relate.

### 2. 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.

### 3. 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.

### 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. How to Construct a Tangent of a Circle

It's pretty amazing what you can draw with just a straight edge and a compass! In this lesson, you'll learn how you can draw tangents of a circle, whether you are given a point on the circle or outside of the circle and if you have two circles.

### 7. 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.

### 8. 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.

### 9. 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.

### 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. Completing the Square Practice Problems

Completing the square is one of the most confusing things you'll be asked to do in an algebra class. Once you get the general idea, it's best to get in there and actually do a few practice problems to make sure you understand the process. Do that here!

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### Other Chapters

Other chapters within the Honors Geometry Textbook course

- Honors Geometry: Foundations of Geometry
- Honors Geometry: Fundamentals of Geometry Proofs
- Honors Geometry: Logic in Mathematics
- Honors Geometry: Introduction to Geometric Figures
- Honors Geometry: Properties of Triangles
- Honors Geometry: Similar & Congruent Triangle Proofs
- Honors Geometry: Right Triangle Proofs
- Honors Geometry: Relationships Within Triangles
- Honors Geometry: Parallel Lines & Polygons
- Honors Geometry: Parallel Line Proofs
- Honors Geometry: Coordinate Geometry
- Honors Geometry: Analytical Geometry
- Honors Geometry: Similar Polygons
- Honors Geometry: Properties of Polygons & Circles
- Honors Geometry: Polygons & Quadrilaterals
- Honors Geometry: Conic Sections
- High School Geometry: Geometric Solids
- Honors Geometry: Introduction to Trigonometry
- Honors Geometry: Right Triangles & Trigonometry
- Honors Geometry: Area, Surface Area & Volume
- Honors Geometry: Perimeter & Circumference
- Honors Geometry: Transformations
- Honors Geometry: Matrices