About This Chapter
Circle Plane Geometry - Chapter Summary
Refresh your understanding of circle plane geometry with this helpful geometry chapter. Our expert math instructors show you basic concepts related to circle plane geometry, including angle and arc measure, circle and cyclic quadrilateral properties, circle graphing and concyclic points. Studying this chapter can help you:
- Recognize the properties of circles and cyclic quadrilaterals
- Use the center, radius and correct formula to graph a circle
- Understand tangent and chord theorems for circles
- Find angle and arc measures using theorems
- Define concyclic points
You'll be able to strengthen your understanding of circle plane geometry by taking the self-assessment quizzes that are included after each lesson. The chapter materials are available 24/7, and you can use any computer or mobile device to access them. Work through the chapter at your own pace, and submit questions to our instructors if you need any extra help.
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. 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.
3. Cyclic Quadrilateral: Definition, Properties & Rules
In this lesson, you will learn about a certain type of geometric shape called a cyclic quadrilateral and discover some properties and rules concerning these shapes.
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. Theorems of Finding Angle & Arc Measures
This lesson explains how to find angle and arc measures. The following theorems are discussed: tangent and intersected chord theorem, angles inside a circle theorem and angles outside a circle theorem.
6. Chord Theorems of Circles in Geometry
Watch this video lesson to learn how a radius will always bisect a perpendicular chord and how equidistant chords will always be congruent to each other. Also, see an example of how you can use these two theorems.
7. Concyclic Points: Definition & Proofs
Concyclic points are points that all lie on the same circle. This lesson will use some useful theorems to explain how to prove whether or not a set of two, three, or four points are concyclic.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards