Angles and Segments in Circles

Stacey Avant, Apr 23, 2018

12.5/12.6 Activity

Table of Contents

  1. Chapter 1: Tangent/Chord (or Secant) Intersections
    1. Part 1: Tangent-Chord Angles
  2. Chapter 2: Angles in Circles
    1. Part 1: Intersecting Chords in a Circle
    2. Part 2: Circle with two secants or one secant/one tangent
  3. Chapter 3: Segments in Circles
    1. Part 1: Segment Lengths in Intersecting Chords
    2. Part 2: Lengths of Segments formed by Intersecting Secants
    3. Part 3: Lengths of Segments formed by one Tangent and one Secant

1.

Chapter 1: Tangent/Chord (or Secant) Intersections

  • 1. Part 1: Tangent-Chord Angles

1.1.

Part 1: Tangent-Chord Angles

Angle JCB is a tangent-chord angle with vertex C.
The vertex of a tangent-chord angle is:
Tangent-Chord Angles
Notice that [math]\angle CAB[/math] and [math]\angle JCB[/math] share a common intercepted arc. What is the relationship between a tangent-chord angle and its intercepted arc?
How is a tangent-chord angle similar to an inscribed angle?
– Stacey Avant, Katie Drach

2.

Chapter 2: Angles in Circles

  • 1. Part 1: Intersecting Chords in a Circle
  • 2. Part 2: Circle with two secants or one secant/one tangent

2.1.

Part 1: Intersecting Chords in a Circle

Investigate the relationship between the angles formed by the two chords and their corresponding arc measures.
– Stacey Avant, Carter McClung, zachhite

2.2.

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3.

Chapter 3: Segments in Circles

  • 1. Part 1: Segment Lengths in Intersecting Chords
  • 2. Part 2: Lengths of Segments formed by Intersecting Secants
  • 3. Part 3: Lengths of Segments formed by one Tangent and one Secant

3.1.

Part 1: Segment Lengths in Intersecting Chords

Investigate the relationship between the pairs of segments formed by two intersecting chords.
– Stacey Avant, Catherine A Eagen

3.2.

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3.3.

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