CK-12 Geometry Concepts

9.9. Segments from Chords http://www.ck12.org

12 · 8 = 10 ·x

96 = 10 x

9. 6 =x

Example B

Findxin the diagram below.

Use the ratio from the Intersecting Chords Theorem. The product of the segments of one chord is equal to the
product of the segments of the other.

x· 15 = 5 · 9

15 x= 45

x= 3

Example C

Solve forx.

a)

b)

Again, we can use the Intersecting Chords Theorem. Set up an equation and solve forx.

a)

8 · 24 = ( 3 x+ 1 )· 12

192 = 36 x+ 12

180 = 36 x

5 =x

b)

32 · 21 = (x− 9 )(x− 13 )

672 =x^2 − 22 x+ 117

0 =x^2 − 22 x− 555

0 = (x− 37 )(x+ 15 )

x= 37 ,− 15

However,x 6 =−15 because length cannot be negative, sox=37.

Watch this video for help with the Examples above.

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CK-12 Foundation: Chapter9SegmentsfromChordsB