Discovering the Circle Properties

tinhel, Luci Howard, Paul Baron, Apr 24, 2018

Use this applet to discover the properties of Circles!

Table of Contents

  1. Circle Similarity
    1. Circle Similarity
  2. Angles of Circles
    1. Angle and Arc Relationship Exploration
    2. Inscribed Angles of a Semicircle
    3. Inscribed Angles Intercepting the Same Arc
    4. Cyclic Quadrilaterals
    5. Arcs Intersecting Chords
  3. Chords
    1. Parallel Lines and Intercepted Arcs
    2. Discovering Chord Properties
    3. Congruent Chords
    4. Perpendicular Lines to Chords of Circles
    5. Congruent Chords and their Central Angles - Large Font
    6. Explore - Chord Length
  4. Sectors/Arc Length
    1. Arc Lengths
    2. Radian Measurements
    3. Convert angles in degrees to radians
    4. Convert angles in radians to degrees
    5. Area of a Sector
  5. Tangent/Secant Properties
    1. Point of Tangency
    2. Tangent Segments
    3. ACCESS - Secants and Tangents
    4. Angles Formed by Secants and Tangents
    5. Tangent meets radius
    6. Explore Tangent Line-Chord Angles (Circles)
    7. Two tangents to a circle
    8. Arcs intercepted by Tangent and Secant
    9. tangent-secant theorem
    10. Arcs Intercepted by Two Secant Lines

1.

Circle Similarity

  • 1. Circle Similarity

1.1.

Circle Similarity

In the diagram below, you have two circles, circle A and Circle B. See if you can transform circle B so that it matches circle A exactly ("sits on" circle A). [br][br]Use the horizontal and vertical sliders to move the center of the transformation of circle B (circle B'). [br][br]Then, use the scale factor slider (sf) to adjust the radius of circle B'. [br][br]Click the double arrows in the upper right corner to reset the activity with a new pair of circles.
1. Were you always able to match the circles?[br][br]2. Are circles always congruent? Explain why or why not, using your experiences in this activity.[br][br]3. Are circles always similar? Explain why or why not, using your experiences in this activity.
– Michael Gillespie, Accesscd

2.

Angles of Circles

Use this applet to discover the properties of Inscribed Angles of a Circle!

  • 1. Angle and Arc Relationship Exploration
  • 2. Inscribed Angles of a Semicircle
  • 3. Inscribed Angles Intercepting the Same Arc
  • 4. Cyclic Quadrilaterals
  • 5. Arcs Intersecting Chords

2.1.

Angle and Arc Relationship Exploration

– swolf_1

2.2.

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2.3.

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2.4.

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2.5.

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3.

Chords

  • 1. Parallel Lines and Intercepted Arcs
  • 2. Discovering Chord Properties
  • 3. Congruent Chords
  • 4. Perpendicular Lines to Chords of Circles
  • 5. Congruent Chords and their Central Angles - Large Font
  • 6. Explore - Chord Length

3.1.

Parallel Lines and Intercepted Arcs

Use this applet to discover the properties of Parallel Lines and Intercepted Arcs on circles!
Parallel Lines and Intercepted Arcs
– tinhel

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Sectors/Arc Length

  • 1. Arc Lengths
  • 2. Radian Measurements
  • 3. Convert angles in degrees to radians
  • 4. Convert angles in radians to degrees
  • 5. Area of a Sector

4.1.

Arc Lengths

– Paul Baron

4.2.

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4.3.

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4.4.

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4.5.

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5.

Tangent/Secant Properties

Use this applet to discover the properties of Tangents and Secants of a Circle!

  • 1. Point of Tangency
  • 2. Tangent Segments
  • 3. ACCESS - Secants and Tangents
  • 4. Angles Formed by Secants and Tangents
  • 5. Tangent meets radius
  • 6. Explore Tangent Line-Chord Angles (Circles)
  • 7. Two tangents to a circle
  • 8. Arcs intercepted by Tangent and Secant
  • 9. tangent-secant theorem
  • 10. Arcs Intercepted by Two Secant Lines

5.1.

Point of Tangency

Use this applet to discover the properties of points of Tangency on a Circle!
Point of Tangency
– tinhel

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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