Circles

Progress
Circle basics
Arc measure
Arc length (degrees)
Quiz 1
5 questions
Introduction to radians
Arc length (radians)
Sectors
Quiz 2
5 questions
Inscribed angles
Inscribed shapes problem solving
Properties of tangents
Quiz 3
5 questions
Standard equation of a circle
Expanded equation of a circle
Quiz 4
5 questions
Constructing regular polygons inscribed in circles
Constructing circumcircles & incircles
Constructing a line tangent to a circle
Unit test
15 questions
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Lessons
Circle basicsArc measureArc length (degrees)Quiz 1Introduction to radiansArc length (radians)SectorsQuiz 2Inscribed anglesInscribed shapes problem solvingProperties of tangentsQuiz 3Standard equation of a circleExpanded equation of a circleQuiz 4Constructing regular polygons inscribed in circlesConstructing circumcircles & incirclesConstructing a line tangent to a circleUnit test
Practice
Quizzes
Unit test
Circle basics
Learn
Circles glossary
Radius, diameter, circumference & π
Proof: all circles are similar
Arc measure
Learn
Intro to arc measure
Finding arc measures
Finding arc measures with equations
Practice
Arc measure
4 questions
Practice
Arc measure with equations
4 questions
Practice
Arc length (degrees)
Learn
Arc length from subtended angle
Subtended angle from arc length
Challenge problems: Arc length 1
Challenge problems: Arc length 2
Practice
Arc length
4 questions
Practice
Identify your areas for growth in these lessons:
Circle basics
Arc measure
Arc length (degrees)
Introduction to radians
Learn
Intro to radians
Radians & degrees
Degrees to radians
Radians to degrees
Practice
Radians & degrees
4 questions
Practice
Arc length (radians)
Learn
Arc length as fraction of circumference
Arc length from subtended angle: radians
Challenge problems: Arc length (radians) 1
Challenge problems: Arc length (radians) 2
Practice
Radians & arc length
7 questions
Practice
Sectors
Learn
Area of a sector
Practice
Area of a sector
4 questions
Practice
Identify your areas for growth in these lessons:
Introduction to radians
Arc length (radians)
Sectors
Inscribed angles
Learn
Inscribed angles
Challenge problems: Inscribed angles
Inscribed angle theorem proof
Inscribed angle theorem proof
Practice
Inscribed angles
4 questions
Practice
Inscribed shapes problem solving
Learn
Proof: Right triangles inscribed in circles
Inscribed shapes: find diameter
Inscribed shapes: angle subtended by diameter
Inscribed shapes: find inscribed angle
Challenge problems: Inscribed shapes
Inscribed quadrilaterals proof
Solving inscribed quadrilaterals
Proof: radius is perpendicular to a chord it bisects
Proof: perpendicular radius bisects chord
Area of inscribed equilateral triangle
Practice
Inscribed shapes
4 questions
Practice
Quiz: Inscribed quadrilaterals
5 questions
Practice
Properties of tangents
Learn
Proof: Radius is perpendicular to tangent line
Determining tangent lines: angles
Determining tangent lines: lengths
Proof: Segments tangent to circle from outside point are congruent
Tangents of circles problem (example 1)
Tangents of circles problem (example 2)
Tangents of circles problem (example 3)
Challenge problems: radius & tangent
Challenge problems: circumscribing shapes
Practice
Tangents of circles problems
4 questions
Practice
Identify your areas for growth in these lessons:
Inscribed angles
Inscribed shapes problem solving
Properties of tangents
Standard equation of a circle
Learn
Features of a circle from its standard equation
Graphing a circle from its standard equation
Writing standard equation of a circle
Practice
Features of a circle from its standard equation
4 questions
Practice
Graph a circle from its standard equation
4 questions
Practice
Write standard equation of a circle
4 questions
Practice
Expanded equation of a circle
Learn
Features of a circle from its expanded equation
Circle equation review
Practice
Features of a circle from its expanded equation
4 questions
Practice
Graph a circle from its expanded equation
4 questions
Practice
Identify your areas for growth in these lessons:
Standard equation of a circle
Expanded equation of a circle
Constructing regular polygons inscribed in circles
Learn
Geometric constructions: circle-inscribed square
Geometric constructions: circle-inscribed equilateral triangle
Geometric constructions: circle-inscribed regular hexagon
Constructing circumcircles & incircles
Learn
Geometric constructions: triangle-inscribing circle
Geometric constructions: triangle-circumscribing circle
Constructing a line tangent to a circle
Learn
Geometric constructions: circle tangent
Geometric constructions: circle tangent (example 2)
Test your understanding of Circles with these 15 questions.
About this unit
Explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents.