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Circles

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  • 1. CIRCLES
  • 2. Definitions
    pg 293
    A circle is the set of all points in a plane equidistant from a given point, called the center.
    B
    r
    O
    r
    r
    C
    A
  • 3. Definitions
    pg 293
    A secant of a circle is a line that intersects the circle in two points.
    A chord of a circle is a segment whose endpoints lie on the circle.
    • In the figure, AB is a chord.
    • 4. Thus, every secant contains a chord.
    B
    A
  • 5. Definitions
    pg 293
    A diameter of a circle is a chord containing the center. It is the longest chord.
    A radius of a circle is a segment from the center to a point on the circle.
    radius
    Radius = AO
    O
    A
    B
    Diameter = AB
    diameter
    What is the relationship between a radius and a diameter?
  • 6. Identify if the following is a radius, diameter, or chord.
    BC
    EI
    FJ
    GD
    GF
    IF
    FH
    DA
    MK
    FM
  • Identify if the following is a radius, diameter, or chord.
    AD
    GF
    EG
    GN
    BM
    GL
    KL
    GK
    EK
    GB
  • Identify if the following is a radius, diameter, or chord.
    JH
    TX
    CL
    GD
    EH
    MN
    VC
    NL
    KP
    CQ
  • TANGENTS LINES TO CIRCLES
  • 34. pg 294
    The interior of a circle is the set of all points of the plane whose distance from the center is less than the radius. (inside)
    Theexterior of a circle is the set of all points of the plane whose distance from the center is greater than the radius. (outside)
    O
    Exterior
    Interior
  • 35. pg 294
    A tangent line to a circle is a line in the plane of the circle that intersects the circle in exactly one point.
    The point where a circle and a tangent intersect is the point of tangency.
  • 36. Tangents and Secants
    Tangents and secants are LINES.
    A tangent line intersects the circle at exactly ONE point.
    A secant line intersects the circle at exactly TWO points.
  • 37. A little extra information
    • The word tangent comes from the Latin word meaning to touch
    • 38. The word secant comes from the Latin word meaning to cut.