Geometric Properties of CIrcles

Wong Jinfa, Feb 27, 2016

Table of Contents

  1. Worksheet 01
    1. 1a. Exploring the perpendicular bisector of a chord
    2. 1b - Perpendicular bisector of chord proof
    3. 1c - Exploring equal chords
    4. 1d - Equal chords proof
    5. 1e - Chords equidistant from center
    6. 1f - Angle bisection
    7. 1g - Chords & Distance
  2. Worksheet 02
    1. 2a - Exploring subtended angles
    2. 2b - Angle at center = 2 angle at circumference
    3. 2c - Angle in Semicircle
    4. 2d - Angle in same segment
    5. Converse of angle in same segment

1.

Worksheet 01

  • 1. 1a. Exploring the perpendicular bisector of a chord
  • 2. 1b - Perpendicular bisector of chord proof
  • 3. 1c - Exploring equal chords
  • 4. 1d - Equal chords proof
  • 5. 1e - Chords equidistant from center
  • 6. 1f - Angle bisection
  • 7. 1g - Chords & Distance

1.1.

1a. Exploring the perpendicular bisector of a chord

1) LEFT CIRCLE You are given a circle centered at O and a chord AB with a midpoint M What is angle OMB/OMA when a perpendicular bisector is drawn? 2) RIGHT CIRCLE Move point M such that angle OMB/OMA is is 90 degrees. What is the length of AM and BM?
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1.7.

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2.

Worksheet 02

  • 1. 2a - Exploring subtended angles
  • 2. 2b - Angle at center = 2 angle at circumference
  • 3. 2c - Angle in Semicircle
  • 4. 2d - Angle in same segment
  • 5. Converse of angle in same segment

2.1.

2a - Exploring subtended angles

Explore the subtended angles to figure out the relationships. Thereafter, try and proof this relationship. (Hint: Exterior angle of a triangle)
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