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Chords, secants and tangents

Chords, secants and tangents. The diameter and radius of a circle are 2 special segments that can be used to find properties of a circle. There are 3 more special segments common to every circle. They are CHORDS, SECANTS, and TANGENTS. Chord.

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Chords, secants and tangents

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  1. Chords, secants and tangents

  2. The diameter and radius of a circle are 2 special segments that can be used to find properties of a circle • There are 3 more special segments common to every circle. • They are CHORDS, SECANTS, and TANGENTS

  3. Chord • A chord is a line segment whose endpoints lie on a circle ( a diameter is also a chord)

  4. SECANT • A secant of a circle is a line that intersects a circle at 2 points.

  5. Tangent • A tangent of a circle is a line in the same plane as the circle that intersects the circle at exactly one point, called the point of tangency

  6. Identify parts of the circle

  7. Theorem 43-1 • If a diameter is perpendicular to a chord, then it bisects the chord and its arcs

  8. Theorem 43-2 • If a diameter bisects a chord other than another diameter, then it is perpendicular to the chord.

  9. Any segment that is a perpendicular bisector of a chord is also a diameter of the circle

  10. Theorem 43-3 • The perpendicular bisector of a chord contains the center of the circle • Every diameter passes through the center of the circle, so the perp. bisector of a chord is also a diameter or a line containing the diameter

  11. All chords that lie the same distance from the center of the circle must be the same length

  12. Theorem 43-4 • In a circle or congruent circles: • Chords equidistant from the center are congruent • Congruent chords are equidistant from the center of the circle

  13. The chords in a circle or 2 congruent circles are equidistant from the center if and only if the chords are congruent.

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