4A Circle Theorems; Click on the links for information, examples of problems, and interactive tools for each of the topics.
Introduction to Circles: Terms and definitions
schoolyourself.org/learn/geometry/circles
Circles and Angles
Central angles schoolyourself.org/learn/geometry/central-angle
Inscribed angles schoolyourself.org/learn/geometry/inscribed-angle
Inscribed Diameter
schoolyourself.org/learn/geometry/inscribed-diameter
schoolyourself.org/learn/geometry/inscribed-diameter
Circumscribed Angles: www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-tangents/v/tangents-of-circles-exercise-examples
Inscribed Quadrilaterals: Prove Opposite sides are supplementary.
schoolyourself.org/learn/geometry/cyclic-quad
schoolyourself.org/learn/geometry/cyclic-quad
Radius is Perpendicular to a Tangent: schoolyourself.org/learn/geometry/circle-lines
Circles and Segments
Two Tangents to a Circle from the same point are Congruent: schoolyourself.org/learn/geometry/congruent-tangents
Solve problems, Tangents and Right Triangles: www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-tangents/v/example-with-tangent-and-radius
4B Arc Length, Sectors and Volume
- Arc Length schoolyourself.org/learn/geometry/arc-degrees
- Sectors: schoolyourself.org/learn/geometry/sector-degrees
- Radians: youtu.be/4vMi3ZzLSug
Informally Prove Area of Circle: www.youtube.com/watch?v=YokKp3pwVFc
Volume
Cavalieri's Principle: schoolyourself.org/learn/geometry/cavalieri-3d
Volume of Sphere: Using Cavalieri's Principle: schoolyourself.org/learn/geometry/sphere-volume
2-D and 3-D Objects
Cross Sections: Practice
Rotating 2-D Objects to make 3-D Objects
Constructions
Tangent to a circle from a point (video): mathopenref.com/consttangents.html
Incenter (Angle Bisectors of each angle of a triangle) illuminations.nctm.org/Activity.aspx?id=6748
Circumcenter (Perpendicular Bisectors of each side of a triangle) illuminations.nctm.org/Activity.aspx?id=6870