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Unit 14: Circles
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.
Circle basics
- Circles glossary (Opens a modal)
- Radius, diameter, circumference & π (Opens a modal)
- Proof: all circles are similar (Opens a modal)
Arc measure
- Intro to arc measure (Opens a modal)
- Finding arc measures (Opens a modal)
- Finding arc measures with equations (Opens a modal)
- Arc measure 4 questions Practice
- Arc measure with equations 4 questions Practice
Arc length (from degrees)
- 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)
- Arc length 4 questions Practice
Introduction to radians
- Intro to radians (Opens a modal)
- Radians & degrees (Opens a modal)
- Degrees to radians (Opens a modal)
- Radians to degrees (Opens a modal)
- Radians & degrees 4 questions Practice
Arc length (from radians)
- 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)
- Radians & arc length 4 questions Practice
- Area of a sector (Opens a modal)
- Area of a sector 4 questions Practice
Inscribed angles
- Inscribed angles (Opens a modal)
- Challenge problems: Inscribed angles (Opens a modal)
- Inscribed angle theorem proof (Opens a modal)
- Inscribed angles 4 questions Practice
Inscribed shapes problem solving
- 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)
- Inscribed shapes 4 questions Practice
- Inscribed quadrilaterals 5 questions Practice
Properties of tangents
- 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)
- Tangents of circles problems 4 questions Practice
Area of inscribed triangle
- 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)
Standard equation of a circle
- 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)
- 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
- Features of a circle from its expanded equation (Opens a modal)
- Circle equation review (Opens a modal)
- Features of a circle from its expanded equation 4 questions Practice
- Graph a circle from its expanded equation 4 questions Practice
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Unit test. Test your understanding of Circles with these NaN questions. Start test. Explore, prove, and apply important properties of circles that have to do with things like arc length, radians, inscribed angles, and tangents.
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