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Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

AB = 19, BC = 10, and CD = 5

figure

A)23

B)53

C)38

D)58

What theorem should I use? And how do I use that theorem?

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AC*BC=CD*(CD+X) –  mathguy May 27 '13 at 23:43
    
proofwiki.org/wiki/Secant_Secant_Theorem and proofwiki.org/wiki/Tangent_Secant_Theorem proves that if you are curious –  mathguy May 27 '13 at 23:45
    
I got 47. What am I doing wrong? 24*10=5*(5+x) Is where I started. –  User18927 May 28 '13 at 0:20
    
47 does not work in your equation... but the equation isn't set up right anyway. What is the length of AC according to the given information? (It's not 24.) –  RecklessReckoner May 28 '13 at 0:32
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1 Answer

up vote 1 down vote accepted

AC = AB + BC = 19 + 10 = 29

if AC*BC=CD*(CD+X), then 29*10 = 5*(5+x)
290 + 25 + 5x
5x = 265
x = 53

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