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

21. 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?

22. Example