Unit 9 - Circles

Ms. Benintendi, Feb 11, 2018

This is a collection of Geogebra tools that demonstrate the concepts and ideas in Chapter 10 of the Geometry book.

Table of Contents

  1. Section 1
    1. CIrcle Terms
    2. Circle Vocabulary Exploration
    3. Inscribed Regular Polygon
  2. Section 2
    1. ACCESS - Circles and Central Angles 1
    2. ACCESS - Circles and Central Angles 2
    3. Arc Lengths (Degrees)
  3. Section 3
    1. Theorem 10.2 Congruent Chords
    2. Theorem 10.3 Perpendicular Lines to Chords of Circles
    3. Chord Bisector Demo
  4. Section 4
    1. Inscribed Angle Demonstration
    2. Inscribed Angles and Intercepted Arcs
    3. ACCESS - Congruent Inscribed Angles
    4. ACCESS - Inscribed right Angles
    5. Cyclic Quadrilaterals
    6. 5-CIR-Theorem #4 Inscribed Quadrilaterals
  5. Section 5
    1. Circle theorem: Radius to tangent
    2. 6 Common Tangents to a Circle
  6. Section 6
    1. Secant-Secant Relationship Inside a Circle
    2. Theorem 11-5-1
    3. Tangent-Secant - 2nd Formula (Angle Measures)
    4. Secant angles exterior of circle
    5. Circle with tangents, find perimeter.
  7. Section 7
    1. Explore - Chord Length
    2. 2 Secants - 1st Formula (Segment Lengths)
    3. ACCESS - Secants and Tangents

1.

Section 1

  • 1. CIrcle Terms
  • 2. Circle Vocabulary Exploration
  • 3. Inscribed Regular Polygon

1.1.

CIrcle Terms

– Laura Penafiel

1.2.

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1.3.

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2.

Section 2

  • 1. ACCESS - Circles and Central Angles 1
  • 2. ACCESS - Circles and Central Angles 2
  • 3. Arc Lengths (Degrees)

2.1.

ACCESS - Circles and Central Angles 1

Angle BAC is a central angle on circle A. BC is the arc associated with angle BAC. It is green as a minor arc and red if it is a major arc. Adjust the ca (central angle) slider to change the measure of the central angle. Drag point B to change the location of the angle. [br][br]1. When is arc BC the smallest? [br]2. For which angle measures is arc BC a minor arc? a major arc?
– Accesscd

2.2.

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2.3.

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3.

Section 3

  • 1. Theorem 10.2 Congruent Chords
  • 2. Theorem 10.3 Perpendicular Lines to Chords of Circles
  • 3. Chord Bisector Demo

3.1.

Theorem 10.2 Congruent Chords

Move the blue points to discover the properties of congruent chords.
Exploring Congruent Chords
– epicbriggs, youngcar, Lance Bledsoe

3.2.

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3.3.

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4.

Section 4

  • 1. Inscribed Angle Demonstration
  • 2. Inscribed Angles and Intercepted Arcs
  • 3. ACCESS - Congruent Inscribed Angles
  • 4. ACCESS - Inscribed right Angles
  • 5. Cyclic Quadrilaterals
  • 6. 5-CIR-Theorem #4 Inscribed Quadrilaterals

4.1.

Inscribed Angle Demonstration

Inscribed Angle Investigation
– kschuma

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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5.

Section 5

  • 1. Circle theorem: Radius to tangent
  • 2. 6 Common Tangents to a Circle

5.1.

Circle theorem: Radius to tangent

Circle theorem: Radius to tangent
Circle theorem: Radius to tangent
– Emma Wilson

5.2.

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6.

Section 6

  • 1. Secant-Secant Relationship Inside a Circle
  • 2. Theorem 11-5-1
  • 3. Tangent-Secant - 2nd Formula (Angle Measures)
  • 4. Secant angles exterior of circle
  • 5. Circle with tangents, find perimeter.

6.1.

Secant-Secant Relationship Inside a Circle

Move the points around and observe the changes in measurement. Then try to answer the question!
– Adam Normand

6.2.

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6.3.

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6.4.

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6.5.

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7.

Section 7

  • 1. Explore - Chord Length
  • 2. 2 Secants - 1st Formula (Segment Lengths)
  • 3. ACCESS - Secants and Tangents

7.1.

Explore - Chord Length

AB and CD are chords that intersect inside circle O. Drag A, B, C, and D to adjust the lines. The text shows the lengths of the segments and their products. How are the products of the segments of the chords related?
– Accesscd

7.2.

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7.3.

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Information