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Module 5: Circles with and without coordinates

Topic A: Central and 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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Proof: Right triangles inscribed in circles
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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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Challenge problems: Inscribed shapes
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Inscribed quadrilaterals proof
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Solving inscribed quadrilaterals
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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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Proof: radius is perpendicular to a chord it bisects
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Proof: perpendicular radius bisects chord
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Practice
Inscribed anglesGet 3 of 4 questions to level up!
Inscribed shapesGet 3 of 4 questions to level up!
Inscribed quadrilateralsGet 4 of 5 questions to level up!

Topic B: Lessons 7-8: Angles and arcs

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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!

Topic B: Lessons 9-10: Arc length and sector area

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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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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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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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Area of a sector
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Practice
Arc lengthGet 3 of 4 questions to level up!
Radians & degreesGet 3 of 4 questions to level up!
Radians & arc lengthGet 5 of 7 questions to level up!
Area of a sectorGet 3 of 4 questions to level up!

Topic C: Secants and 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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Geometric constructions: circle tangent
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Geometric constructions: circle tangent (example 2)
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Lessons 14-16: No content yet
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Practice
Tangents of circles problemsGet 3 of 4 questions to level up!

Topic D: Equations for circles and their tangents

Learn
Features of a circle from its standard equation
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Graphing a circle from its standard equation
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Writing standard equation of a circle
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Features of a circle from its expanded equation
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Circle equation review
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Lesson 19: No content yet
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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!
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!

Topic E: Cyclic quadrilaterals and Ptolemy’s theorem

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Topic E: No content yet
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About this unit

"This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied throughout the year. It also includes the specific properties of triangles, special quadrilaterals, parallel lines and transversals, and rigid motions established and built upon throughout this mathematical story. This module's focus is on the possible geometric relationships between a pair of intersecting lines and a circle drawn on the page." Eureka Math/EngageNY (c) 2015 GreatMinds.org