## 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

**Introduction to Circles:**

**Circles and Angles**

**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**

**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