Answer:
39
Step-by-step explanation:
The chords are equal to eachother. First multiply their divided lengths together:
9(3x-9)=21(x+1)
27x-81=21x+21
x=17
CD= 21+x+1
21+17+1=39
CD= 39
Chords AB and CD intersect as shown in the given figure. The chords are equal to each other. The length of CD is 17.
If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing into two equal parts) the line segment AB.
Or
|AC| = |CB|
Chords AB and CD intersect as shown below.
The chords are equal to each other.
Therefore,
[tex]9(3x-9)=21(x+1)\\27x - 81 = 21x + 21\\\\27x - 21x= 81 + 21\\\\x= 17[/tex]
CD = 21 + x + 1
21 + 17 + 1 = 39
CD = 39
Learn more about the chord of a circle here:
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