Day two: The properties of Chord in Circles

by Nami Youn

To discover the relationship of the center angle and the chord

To understand the properties of the perpendicular bisector of the chord

To find the distance from the center of a circle to the chord

1. The center angle, Arc, and Chord


Property 1 : In a circle.  the length of arc (or chord) with the same central angle is always the same.
Also, in the congruent circles, this property is satisfied.

Gsp file

Property 2 : The length of  an arc is proportional to the center angle of the circle.
 But, the length of a chord is not.

GSP file

2. The perpendicular bisector of a chord.

Property : The perpendicular line from the center to the chord of a circle bisects this chord.
The perpendicular bisector of a chord in a circle passes through the center of the circle.

Gsp file

3. The length of a chord

Property : If from the center of a circle, the distance to a chord is equal to that of another chord in a circle, two chords have the same length.

Gsp file


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