# Ch 22: Circles: NBPTS Math - Adolescence & Young Adult

### About This Chapter

## Circles: NBPTS Math - Adolescence & Young Adult - Chapter Summary

In the lessons of this chapter, our professional instructors will help you improve your skills in solving mathematical problems involving circles. After these lessons, you should be better prepared for questions on the National Board for Professional Teaching Standards (NBPTS) Adolescence and Young Adulthood/Mathematics certificate exam that will ask you to:

- Find the circumference of a circle using its diameter and Pi
- Identify the different parts of circles
- Use the theorems of tangents of circles
- Measure major arcs, minor arcs and chords of circles
- Calculate the area of sectors
- Find the properties of inscribed angles, inscribed figures and circumscribed figures
- Measure angles and lengths involving tangents, chords and secants
- Identify the equation of a circle

Study the key vocabulary while you review these lessons, and take the lesson quizzes to discover topics you don't understand. In the video lessons, use the tags to return to and study the parts of the lessons that explain them. If you come across a topic that confuses you, ask our instructors for assistance using the 'teacher' tabs of the lessons.

### 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. Diameter and Circumference Related with Pi

After watching this video, you will be able to tell others how the number pi is related to a circle's diameter and circumference. And using your newfound knowledge, you will be able to calculate the circumference or diameter of a circle.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. Finding the Area of a Sector: Formula & Practice Problems

In this lesson, you'll review your knowledge of circle vocabulary and then discover how to calculate the area of a sector of a circle. The lesson covers finding the area of the sector using degrees and radians.

### 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. 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. 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.

### 11. 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.

### 12. 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 National Board Certification Exam - Mathematics/Adolescence & Young Adulthood: Practice & Study Guide course

- Teaching Math: NBPTS Math - Adolescence & Young Adult
- Understanding Math: NBPTS Math - Adolescence & Young Adult
- Numbers: NBPTS Math - Adolescence & Young Adult
- Operations: NBPTS Math - Adolescence & Young Adult
- Algebraic Reasoning: NBPTS Math - Adolescence & Young Adult
- Equations: NBPTS Math - Adolescence & Young Adult
- Systems of Equations: NBPTS Math - Adolescence & Young Adult
- Inequalities: NBPTS Math - Adolescence & Young Adult
- Functions: NBPTS Math - Adolescence & Young Adult
- Exponents & Exponential Functions: NBPTS Math - Adolescence & Young Adult
- Logarithmic Functions: NBPTS Math - Adolescence & Young Adult
- Rational Functions: NBPTS Math - Adolescence & Young Adult
- Quadratic Functions: NBPTS Math - Adolescence & Young Adult
- Trigonometric Functions: NBPTS Math - Adolescence & Young Adult
- Polynomials: NBPTS Math - Adolescence & Young Adult
- Series & Sequences: NBPTS Math - Adolescence & Young Adult
- Geometry Concepts: NBPTS Math - Adolescence & Young Adult
- Lines: NBPTS Math - Adolescence & Young Adult
- Angles: NBPTS Math - Adolescence & Young Adult
- Transformations: NBPTS Math - Adolescence & Young Adult
- Congruence & Similarity: NBPTS Math - Adolescence & Young Adult
- Area & Volume: NBPTS Math - Adolescence & Young Adult
- Trigonometry: NBPTS Math - Adolescence & Young Adult
- Discrete Mathematics: NBPTS Math - Adolescence & Young Adult
- Data Analysis & Statistics: NBPTS Math - Adolescence & Young Adult
- Probability: NBPTS Math - Adolescence & Young Adult
- Calculus: NBPTS Math - Adolescence & Young Adult
- Student Development: NBPTS Math - Adolescence & Young Adult
- Practice of Teaching: NBPTS Math - Adolescence & Young Adult
- Learning Environments: NBPTS Math - Adolescence & Young Adult
- Thinking Mathematically: NBPTS Math - Adolescence & Young Adult
- Assessment: NBPTS Math - Adolescence & Young Adult
- Reflection & Growth: NBPTS Math - Adolescence & Young Adult
- Families & Communities: NBPTS Math - Adolescence & Young Adult
- Professional Community: NBPTS Math - Adolescence & Young Adult
- National Board Certification Exam - Mathematics/Adolescence & Young Adulthood Flashcards