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Congruent Chords of Circles 
Equidistant from Center
In the same circle or in congruent circles
- chords equidistant from the center of a circle are congruent
- congruent chords are equidistant from the center
- the perpendicular bisector of a chord contains the center of the circle
If XY is 10, what is the length of AB?
Chord AB
AB =10
The two chords below are congruent.
If YX = 6 and the radius of the circle is 5, what is the distance from the center of the circle to either chord?
We can use the good old pythagorean theorem.
52=32+x2
x = 4
The two chords below are equidistant from the center of the circle.
The blue line on the left is perpendicular to the two chords. The radius of the circle is 25. How large is X?
What is the length of either of the chords?
x2+ 72=252
x = 24
Chord =2
× 24 = 48
How Large is the radius of the circle on the left? The chords are equidistant from the center of the circle.
142+482=r2
r=50
Are the two chords in the picture below congruent?
Answer
No, not necessarilly. Although the one chord is bisected we do not kow that the two chords are equidistant from the center.
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