About This Chapter
Circles - Chapter Summary
Continue your study of plane geometry with this chapter on circles. Our experienced instructors can help you study the properties of circles and provide you with tips for proving their similarity. You can also examine the radii, tangents and chords that intersect them.
Lessons showing you how to find the lengths of chords and the inscribed angles of tangents are included as well. You can also explore the relationship between arcs and radians and practice calculating the area of a sector. Additional lessons help you apply these skills when working with inscribed and circumscribed triangles and quadrilaterals.
Instructors go on to break down the formula for a circle and show you how to write it when presented with a circle's center and radius. You can also learn how to find the center and radius when given a circle's equation by completing the square. Topics of discussion found in this chapter include:
- Inscribed angles
- Radii and chords
- Arc length
Take advantage of the illustrations included in this chapter's video lessons to get the hang of working with circles. This same material is also presented in the form of transcripts that feature links to supplementary text lessons. Use them to discover definitions of key terms and improve your understanding of the lesson topics. There are also multiple-choice quizzes you can take at any point during your studies in order to assess your grasp of the material.
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. Inscribed Angle: Definition, Theorem & Formula
Circles are all around us in our world. Inscribed angles are angles that sit inside a circle with the vertex on the circumference of the circle. Inscribed angles have a special relationship with the intercepted arc.
3. How to Find the Radius of a Circle: Definition & Formula
In this lesson, you will discover the definition of a radius. You will also learn how to find the radius of a circle using three different formulas based on diameter, circumference, and area.
4. What is a Chord in Math?
In this lesson, you will learn what a chord of a circle is in math. You will also learn other basic parts of a circle, including the diameter and radius. Finally, you will see which of these parts is a chord and which is not.
5. 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.
6. 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.
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Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course
- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards