# 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

A circle has two dimensions and four shapes, each with a different function. Explore the definition, see examples, and discover the four parts of a circle including the center, radius, diameter, and chords.

### 2. 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.

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

The chord of a circle can be used to measure the circumference of a shape. Learn how to identify the chord and describe the difference between it, a diameter, and a secant, and use formulas to determine a chord's length.

### 4. Circular Arcs and Circles: Definitions and Examples

A circle is defined as a set of points that are equidistant from a central point, while a circular arc is a part of the circumference of a circle. Explore the definition of a locus and find examples of circles and minor and major circular arcs.

### 5. 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.

### 6. 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.

### 7. Converting Between Radians and Degrees

The two most widely used units of measure for angles are degrees and radians. Learn how to convert radians to degrees and degrees to radians using the concepts of proportion and priority.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. Circumscribed Angle: Definition & Theorem

Learn about circumscribed angles, what they are, and the theorem for circumscribed angles. Discover how circumscribed angles are created by two intersecting tangent lines and how to use radii and tangent lines to make quadrilaterals.

### 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

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.

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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