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Circle basics

Learn
Circles glossary
(Opens a modal)
Radius, diameter, circumference & π
(Opens a modal)
Proof: all circles are similar
(Opens a modal)

Arc measure

Learn
Intro to arc measure
(Opens a modal)
Finding arc measures
(Opens a modal)
Finding arc measures with equations
(Opens a modal)
Practice
Arc measureGet 3 of 4 questions to level up!
Arc measure with equationsGet 3 of 4 questions to level up!

Arc length (from degrees)

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Arc length from subtended angle
(Opens a modal)
Subtended angle from arc length
(Opens a modal)
Challenge problems: Arc length 1
(Opens a modal)
Challenge problems: Arc length 2
(Opens a modal)
Practice
Arc lengthGet 3 of 4 questions to level up!

Introduction to radians

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Intro to radians
(Opens a modal)
Radians & degrees
(Opens a modal)
Degrees to radians
(Opens a modal)
Radians to degrees
(Opens a modal)
Practice
Radians & degreesGet 3 of 4 questions to level up!

Arc length (from radians)

Learn
Arc length as fraction of circumference
(Opens a modal)
Arc length from subtended angle: radians
(Opens a modal)
Challenge problems: Arc length (radians) 1
(Opens a modal)
Challenge problems: Arc length (radians) 2
(Opens a modal)
Practice
Radians & arc lengthGet 5 of 7 questions to level up!

Sectors

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Area of a sector
(Opens a modal)
Practice
Area of a sectorGet 3 of 4 questions to level up!

Inscribed angles

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Inscribed angles
(Opens a modal)
Challenge problems: Inscribed angles
(Opens a modal)
Inscribed angle theorem proof
(Opens a modal)
Inscribed angle theorem proof
(Opens a modal)
Practice
Inscribed anglesGet 3 of 4 questions to level up!

Inscribed shapes problem solving

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Proof: Right triangles inscribed in circles
(Opens a modal)
Inscribed shapes: find diameter
(Opens a modal)
Inscribed shapes: angle subtended by diameter
(Opens a modal)
Inscribed shapes: find inscribed angle
(Opens a modal)
Challenge problems: Inscribed shapes
(Opens a modal)
Inscribed quadrilaterals proof
(Opens a modal)
Solving inscribed quadrilaterals
(Opens a modal)
Proof: radius is perpendicular to a chord it bisects
(Opens a modal)
Proof: perpendicular radius bisects chord
(Opens a modal)
Area of inscribed equilateral triangle
(Opens a modal)
Practice
Inscribed shapesGet 3 of 4 questions to level up!
Inscribed quadrilateralsGet 4 of 5 questions to level up!

Properties of tangents

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Proof: Radius is perpendicular to tangent line
(Opens a modal)
Determining tangent lines: angles
(Opens a modal)
Determining tangent lines: lengths
(Opens a modal)
Proof: Segments tangent to circle from outside point are congruent
(Opens a modal)
Tangents of circles problem (example 1)
(Opens a modal)
Tangents of circles problem (example 2)
(Opens a modal)
Tangents of circles problem (example 3)
(Opens a modal)
Challenge problems: radius & tangent
(Opens a modal)
Challenge problems: circumscribing shapes
(Opens a modal)
Practice
Tangents of circles problemsGet 3 of 4 questions to level up!

Standard equation of a circle

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Features of a circle from its standard equation
(Opens a modal)
Graphing a circle from its standard equation
(Opens a modal)
Writing standard equation of a circle
(Opens a modal)
Practice
Features of a circle from its standard equationGet 3 of 4 questions to level up!
Graph a circle from its standard equationGet 3 of 4 questions to level up!
Write standard equation of a circleGet 3 of 4 questions to level up!

Expanded equation of a circle

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Features of a circle from its expanded equation
(Opens a modal)
Circle equation review
(Opens a modal)
Practice
Features of a circle from its expanded equationGet 3 of 4 questions to level up!
Graph a circle from its expanded equationGet 3 of 4 questions to level up!

Constructing regular polygons inscribed in circles

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Geometric constructions: circle-inscribed square
(Opens a modal)
Geometric constructions: circle-inscribed equilateral triangle
(Opens a modal)
Geometric constructions: circle-inscribed regular hexagon
(Opens a modal)

Constructing circumcircles & incircles

Learn
Geometric constructions: triangle-inscribing circle
(Opens a modal)
Geometric constructions: triangle-circumscribing circle
(Opens a modal)

Constructing a line tangent to a circle

Learn
Geometric constructions: circle tangent
(Opens a modal)
Geometric constructions: circle tangent (example 2)
(Opens a modal)

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.