# Ch 39: PLACE Mathematics: Circular Arcs & Circles

### About This Chapter

## PLACE Mathematics: Circular Arcs and Circles - Chapter Summary

The lessons in this chapter give you the opportunity to review concepts related to circles and solving math problems that incorporate them. Some of the topics you'll see in this chapter include:

- Finding the area and circumference of a circle
- Identifying circular arcs and central and inscribed angles
- Measuring arcs and inscribed angles
- Tangent of a circle theorems
- Using tangents, chords and secants when measuring angles and lengths
- Finding area using arc length of a sector

Our experienced instructors lead you through each lesson and provide easy techniques for remembering how to solve problems with circles. Transcripts are also available that highlight key terms you'll need to know.

### Objectives of the PLACE Mathematics: Circular Arcs and Circles Chapter

The PLACE Mathematics test may include questions that analyze your comprehension of the different ways to calculate measurements of circles and their parts. The topic in this Circular Arcs and Circles chapter can be found within the Measurement and Geometry section of the PLACE Mathematics exam, which makes up approximately 19% of the total test.

There are about 100 questions on the total test and all are multiple choice. You can practice answering questions similar to those you will see on the test by using our multiple-choice quizzes at the end of each lesson.

### 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. 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.

### 3. Central and Inscribed Angles: Definitions and Examples

A circle's central angles are formed by two radii, and inscribed angles are formed from two points on the circumference. Explore the definitions of these two concepts and tackle example problems involving calculating central and inscribed angles.

### 4. Measure of an Arc: Process & Practice

The measure of an arc can be solved by determining the degree of the angle that intercepts an arc. Learn about the process of measuring an arc, major vs. minor arcs, and real-world practice arc problems.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

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### Other Chapters

Other chapters within the PLACE Mathematics: Practice & Study Guide course

- PLACE Mathematics: Properties of Real Numbers
- PLACE Mathematics: Fractions
- PLACE Mathematics: Decimals & Percents
- PLACE Mathematics: Ratios & Proportions
- PLACE Mathematics: Measurements & Conversions
- PLACE Mathematics: Logic
- PLACE Mathematics: Mathematical Reasoning
- PLACE Mathematics: Vector Operations
- PLACE Mathematics: Matrices & Determinants
- PLACE Mathematics: Exponents & Exponential Expressions
- PLACE Mathematics: Algebraic Expressions
- PLACE Mathematics: Linear Equations
- PLACE Mathematics: Inequalities
- PLACE Mathematics: Absolute Value Problems
- PLACE Mathematics: Quadratic Equations
- PLACE Mathematics: Polynomials
- PLACE Mathematics: Rational Expressions
- PLACE Mathematics: Radical Expressions
- PLACE Mathematics: Systems of Equations
- PLACE Mathematics: Complex Numbers
- PLACE Mathematics: Functions
- PLACE Mathematics: Graphing Piecewise Functions
- PLACE Mathematics: Exponential and Logarithmic Functions
- PLACE Mathematics: Continuity of Functions
- PLACE Mathematics: Limits
- PLACE Mathematics: Rate of Change
- PLACE Mathematics: Calculating Derivatives & Derivative Rules
- PLACE Mathematics: Graphing Derivatives & L'Hopital's Rule
- PLACE Mathematics: Applications of Derivatives
- PLACE Mathematics: Area Under the Curve & Integrals
- PLACE Mathematics: Integration & Integration Techniques
- PLACE Mathematics: Integration Applications
- PLACE Mathematics: Foundations of Geometry
- PLACE Mathematics: Introduction to Geometric Figures
- PLACE Mathematics: Properties of Triangles
- PLACE Mathematics: Triangles, Theorems & Proofs
- PLACE Mathematics: Parallel Lines & Polygons
- PLACE Mathematics: Quadrilaterals
- PLACE Mathematics: Conic Sections
- PLACE Mathematics: Geometric Solids
- PLACE Mathematics: Analytical Geometry
- PLACE Mathematics: Using Trigonometric Functions
- PLACE Mathematics: Trigonometric Graphs
- PLACE Mathematics: Solving Trigonometric Equations
- PLACE Mathematics: Trigonometric Identities
- PLACE Mathematics: Sequences & Series
- PLACE Mathematics: Graph Theory
- PLACE Mathematics: Set Theory
- PLACE Mathematics: Overview of Statistics
- PLACE Mathematics: Summarizing Data
- PLACE Mathematics: Tables & Plots
- PLACE Mathematics: Probability
- PLACE Mathematics: Discrete Probability Distributions
- PLACE Mathematics: Continuous Probability Distributions
- PLACE Mathematics: Sampling
- PLACE Mathematics: Hypothesis Testing
- PLACE Mathematics: Regression & Correlation
- PLACE Mathematics Flashcards