Circles and Chords

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Questions and Answers

Which of the following statements about a chord is true?

  • A chord is a line segment that connects the center of a circle to a point on the circle.
  • A chord is a line segment that connects two points on a circle.
  • A chord is any segment with endpoints that are on the circle. (correct)
  • A chord is formed by the intersection of two arcs on a circle.

What is the relationship between congruent chords and congruent arcs in the same circle?

  • Congruent chords in the same circle intersect at the center of the circle.
  • Congruent chords in the same circle have equal lengths.
  • Congruent chords in the same circle have perpendicular bisectors.
  • Congruent chords in the same circle have congruent corresponding arcs. (correct)

If a diameter of a circle is perpendicular to a chord, what can be concluded about the relationship between the diameter, chord, and their respective arcs?

  • The diameter is equal in length to the chord.
  • The diameter is parallel to the chord.
  • The diameter bisects the chord and its arc. (correct)
  • The diameter and chord intersect at the center of the circle.

What can be concluded if one chord is a perpendicular bisector of another chord in a circle?

<p>The first chord is a diameter of the circle. (B)</p> Signup and view all the answers

What is the measure of angle AD in the given diagram?

<p>40° (D)</p> Signup and view all the answers

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Study Notes

Circle Chords and Arcs

  • Congruent chords in the same circle have congruent arcs.
  • If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and the respective arcs.
  • If one chord is a perpendicular bisector of another chord in a circle, then the two chords are perpendicular bisectors of each other.
  • In the given diagram, angle AD is a right angle (90 degrees).

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