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Circle basics

Learn
Getting ready for circles
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Circles glossary
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Area of a circle intuition
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Proof: all circles are similar
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Arc measure

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Intro to arc measure
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Finding arc measures
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Finding arc measures with equations
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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)

Learn
Arc length from subtended angle
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Subtended angle from arc length
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Challenge problems: Arc length 1
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Challenge problems: Arc length 2
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Practice
Arc lengthGet 3 of 4 questions to level up!

Quiz 1

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Introduction to radians

Learn
Radians as ratio of arc length to radius
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Arcs, ratios, and radians
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Intro to radians
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Radians & degrees
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Degrees to radians
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Radians to degrees
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Practice
Radians & degreesGet 3 of 4 questions to level up!

Arc length (from radians)

Learn
Arc length as fraction of circumference
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Arc length from subtended angle: radians
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Challenge problems: Arc length (radians) 1
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Challenge problems: Arc length (radians) 2
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Practice
Radians & arc lengthGet 3 of 4 questions to level up!

Sectors

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Area of a sector
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Practice
Area of a sectorGet 3 of 4 questions to level up!

Quiz 2

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Inscribed angles

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Inscribed angles
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Challenge problems: Inscribed angles
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Inscribed angle theorem proof
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Inscribed angle theorem proof
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Practice
Inscribed anglesGet 3 of 4 questions to level up!

Inscribed shapes problem solving

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Inscribed shapes: find diameter
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Inscribed shapes: angle subtended by diameter
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Inscribed shapes: find inscribed angle
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Solving inscribed quadrilaterals
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Challenge problems: Inscribed shapes
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Practice
Inscribed shapesGet 3 of 4 questions to level up!

Proofs with inscribed shapes

Learn
Proof: Right triangles inscribed in circles
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Inscribed quadrilaterals proof
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Proof: radius is perpendicular to a chord it bisects
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Proof: perpendicular radius bisects chord
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Properties of tangents

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

Quiz 3

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Constructing regular polygons inscribed in circles

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Geometric constructions: circle-inscribed square
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Geometric constructions: circle-inscribed equilateral triangle
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Geometric constructions: circle-inscribed regular hexagon
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Constructing circumcircles & incircles

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Geometric constructions: triangle-inscribing circle
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Geometric constructions: triangle-circumscribing circle
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Constructing a line tangent to a circle

Learn
Geometric constructions: circle tangent
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Geometric constructions: circle tangent (example 2)
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Unit test

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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.