Properties of Chords

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

Property #1:

Chords that are equidistant from the center of a circle are equal in length.

If OE = OG , then AB = CD.

Converse of Property #1:

Equal chords are equidistant from the center of a circle.

If AB = CD , then OE = OG.

Property #2:All radii of a circle are equal.

OA = OC = OD

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

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

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

Property #4

Equal chords have equal arcs.

Converse of Property #4

Equal arcs have equal chords.

Example

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

Example

Example

ExampleIn 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?

Example

Example

Example