# Ch 30: Circular Arcs, Circles & Angles: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering high school trigonometry material will benefit from taking this course. There is no faster or easier way to learn high school trigonometry. Among those who would benefit are:

- Students who have fallen behind in understanding how to find the measures of angles, arcs, tangents and secants created by inscribed and circumscribed figures
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about circular arcs, circles and angles
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Circular Arcs, Circles & Angles chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know, review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Circular Arcs, Circles & Angles chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any circular arcs, circles and angles question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

In this chapter, you'll learn the answer to questions including:

- How do I calculate the area and circumference of a circle?
- What are inscribed angles, radii and chords?
- What are inscribed and circumscribed figures?
- How do I execute proofs for inscribed quadrilaterals and triangles?
- What are circle tangents and sectors?
- How can I use the equation of a circle?
- What are the parts of regular polygons?

### 1. Circles: Area and Circumference

Like all geometric shapes, circles take up space and a formula is required to calculate the area. Learn about the area and circumference of circles, explore the formula to calculate a circle's area, and review examples that use the diameter and others that use the circumference to find the area of a circle.

### 2. Inscribed and Circumscribed Figures: Definition & Construction

Inscribed figures are shapes drawn in other shapes while circumscribed figures are shapes drawn outside other shapes. Study the definition and construction of inscribed polygons and circles and circumscribed figures, and find practice problems.

### 3. How to Find the Measure of an Inscribed Angle

An inscribed angle occurs when two lines, or chords, share an endpoint. Explore this idea in depth, unpacking how to use central angles and arc lengths to determine the measure of the inscribed angles.

### 4. Tangent of a Circle: Definition & Theorems

The tangent of a circle is a line that touches the circle in only one place, making it unable to enter the circle. Learn about different theorems of tangent circles through geometric examples.

### 5. Arc Length of a Sector: Definition and Area

Sectors are a part of a circle which meets in the center and has an arch connecting the two straight lengths, or radii: they are shaped much like slices of pizza. Learn how to calculate the arc length of a sector and the formula behind determining the given area.

### 6. Measurements of Angles Involving Tangents, Chords & Secants

An angle refers to the space that is created when two lines intersect or meet. Learn how to calculate measurements about angles that are created by tangents, chords, and secants in a circle, including two chords, tangent and chord, two tangent lines, tangent and secant, and two secant lines.

### 7. Measurements of Lengths Involving Tangents, Chords and Secants

A circle has measurements of lengths that intersect at different points on the curve. Learn about intersecting chords, secants, and tangents and their relationship to each other on the circle.

### 8. Regular Polygons: Definition & Parts

Polygons are two dimensional shapes with straight sides, and regular polygons are those with all equal sides and angles. Learn the differences between regular and irregular polygons and the various parts that are used to create them.

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

In mathematics, circles have two forms of equations. Learn how to find the equation of a circle. Recognize that circle equations have a standard form, as well as a general form, and explore several examples to gain an understanding of each form.

### 10. Radian Measure: Definition & Formula

In mathematics, the radian is the standard unit of angular measure. This lesson will define radian and work through some problems involving radians. The lesson will end with a quiz.

### 11. Radians and Degrees: Definition & Examples

Radians and degrees are used to measure and describe angles. Learn the distinction between the two by looking at their definitions and examples as well as the importance of these two in mathematical problems.

### 12. Reflex Angle: Definition & Examples

A reflex angle is any angle measured between 180º and 360º added to an acute or obtuse angle to complete a full 360º circle. See example problems and solutions demonstrating the use of reflex angles, as well as how to measure them.

### 13. Segment Bisector: Definition & Example

A segment bisector passes through a midpoint and cuts a line segment into two equal parts. Learn the definition of segment bisectors, discover facts that should be considered when working with segment bisectors, and look at some examples.

### 14. Perimeter of a Sector of a Circle

The perimeter is a measure of the distance along the edge of an object, which can be calculated even for partial slices of a circle, known as sectors. Learn how the radius and arc length are both used to calculate the perimeter, demonstrated in an example.

### Earning College Credit

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### Other Chapters

Other chapters within the High School Trigonometry: Help and Review course

- Real Numbers - Types and Properties: Help and Review
- Working with Linear Equations in Trigonometry: Help and Review
- Working with Inequalities in Trigonometry: Help and Review
- Absolute Value Equations in Trigonometry: Help and Review
- Working with Complex Numbers in Trigonometry: Help and Review
- Systems of Linear Equations in Trigonometry: Help and Review
- Mathematical Modeling in Trigonometry: Help and Review
- Introduction to Quadratics in Trigonometry: Help and Review
- Working with Quadratic Functions in Trigonometry: Help and Review
- Coordinate Geometry Review: Help and Review
- Functions for Trigonometry: Help and Review
- Understanding Function Operations in Trigonometry: Help and Review
- Graph Symmetry in Trigonometry: Help and Review
- Graphing with Functions in Trigonometry: Help and Review
- Basic Polynomial Functions in Trigonometry: Help and Review
- Higher-Degree Polynomial Functions in Trigonometry: Help and Review
- Rational Functions in Trigonometry: Help and Review
- Trig - Rational Expressions & Function Graphs: Help & Review
- Exponential & Logarithmic Functions in Trigonometry: Help and Review
- Trigonometric Functions: Help and Review
- Geometry in Trigonometry: Help and Review
- Triangle Trigonometry: Help and Review
- Working with Trigonometric Graphs: Help and Review
- Trigonometric Equations: Help and Review
- Working with Trigonometric Identities: Help and Review
- Applications of Trigonometry: Help and Review
- Analytic Geometry & Conic Sections in Trigonometry: Help and Review
- Vectors, Matrices & Determinants in Trigonometry: Help and Review
- Polar Coordinates & Parameterizations: Help and Review
- TASC Math: Trigonometry