Properties of Chords

1. Properties of Chords

2. When a chord intersects the circumference of a circle certain properties will be true.

3. Property #1: Chords that are equidistant from the center of a circle are equal in length. If OE = OG , then AB = CD.

4. Converse of Property #1: Equal chords are equidistant from the center of a circle. If AB = CD , then OE = OG.

5. Property #2: All radii of a circle are equal. OA = OC = OD

6. Property #3: A line from the center of a circle, perpendicular to a chord, bisects the chord (and the subtended arc).

7. Converse of Property #3: If the line that is perpendicular to a chord bisects the chord, then the line passes through the center of the circle.

8. Another Converse of Property #3: If a line passing through the center bisects a chord (or its arc), then it is perpendicular to the chord.

9. Property #4 Equal chords have equal arcs.

10. Converse of Property #4 Equal arcs have equal chords.

18. Example What is the distance between the two parallel chords if the radius of the circle is 7?

19. Example

20. Example

21. Example In a circle with radius 7 cm, a chord is 3 cm from the center. How long is another chord located 3 cm from the center?

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