Chord properties

Chord properties

In a circle, when a line passes through the center of the circle and is perpendicular to a chord, the line will bisect the chord. In other words, the perpendicular bisector of a chord always passes through the center of the circle.
Basic Concepts: Angles in a circle, Tangent properties, Circles and circumference
Related Concepts: Arcs of a circle, Areas and sectors of circles, Circle chord, tangent, and inscribed angles proofs

Lessons

  • Introduction
    a)
    1. What is a chord?
    2. What is a tangent?

    b)
    What are the properties of a chord?

  • 1.
    If AC is 4 cm and BD is 15 cm, what is the diameter of the circle?
    using chord properties to determine diameter
  • 2.
    Zoe wants to set up her round dining table by putting a candle in the centre of it. How can she do that by using a tangent? Explain your answer with a diagram.
  • 3.
    Below is a segment of a circle, and A is the center of the circle. The radius is 15 cm, BC is 7.5 cm, and DE is 24 cm.
    Using chord properties to find radius and other unknowns
    Determine.
    a)
    ∠\angleCED

    b)
    CE

    c)
    BE

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10.
Circle Geometry
10.1
Angles in a circle
10.2
Chord properties
10.3
Tangent properties
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