CK-12 Geometry Concepts

9.4. Chords in Circles http://www.ck12.org

Because the diameter is perpendicular to the chord, it also bisects the chord and the arc. Set up an equation forxand
y.

( 3 x− 4 )◦= ( 5 x− 18 )◦ y+ 4 = 2 y+ 1

14 ◦= 2 x 3 =y

7 ◦=x

Watch this video for help with the Examples above.

MEDIA

Click image to the left for more content.

CK-12 Foundation: Chapter9ChordsinCirclesB

Concept Problem Revisited

In the picture, the chords from
⊙
Aand
⊙
Eare congruent and the chords from
⊙
B,
⊙
C, and
⊙
Dare also
congruent. We know this from Chord Theorem #1. All five chords are not congruent because all five circles are not
congruent, even though the central angle for the circles is the same.

Vocabulary

Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Aradiusis
the distance from the center to the outer rim of a circle. Achordis a line segment whose endpoints are on a circle.
Adiameteris a chord that passes through the center of the circle.

Guided Practice

1. Is the converse of Chord Theorem #2 true?


2. Find the value ofx.

3.BD=12 andAC=3 in

⊙

A. Find the radius andmBD̂.

Answers:

1. The converse of Chord Theorem #2 would be: A diameter is also the perpendicular bisector of a chord. This is
   not a true statement, see the counterexample to the right.


2. Because the distance from the center to the chords is congruent and perpendicular to the chords, then the chords
   are equal.

6 x− 7 = 35

6 x= 42

x= 7