Chords, secants, and tangents are shown. State the equation you would use to find the value of x. Then solve for x.

*Please wait while I draw the diagram*

Question

Chords, secants, and tangents are shown. State the equation you would use to find the value of x. Then solve for x. 

*Please wait while I draw the diagram*

whitemonsterbunny17 · Answer

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whitemonsterbunny17 · Answer

What I don't get is how to find x. What the equation would be. I couldn't find anything in the book that would help.

nincompoop · Answer

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nincompoop · Answer

$\huge a^2 = bc $

whitemonsterbunny17 · Answer

But how do I figure out what a squared is?

nincompoop · Answer

think around these lines 
$a+b = 9 $

nincompoop · Answer

clever, right?

whitemonsterbunny17 · Answer

Oh, so each is half of 9, right?

nincompoop · Answer

we cannot assume that it is HALF

whitemonsterbunny17 · Answer

If we can't assume it is half, then how do we know which is which?

nincompoop · Answer

i drew it incorectly, sorry

nincompoop · Answer

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nincompoop · Answer

$\huge bx = a^2$

whitemonsterbunny17 · Answer

Okay, so
$\Large\bf\color{black}{bx=36}$

whitemonsterbunny17 · Answer

How do I get rid of b?

whitemonsterbunny17 · Answer

(Sorry, I know I'm a pain.)

nincompoop · Answer

no... 
x = 9

a + b = x = 9
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whitemonsterbunny17 · Answer

How does x=9?

nincompoop · Answer

you gave the value x =9

nincompoop · Answer

unless your x is just the external secant

whitemonsterbunny17 · Answer

Oh.
I was seeing x as just half of 9 rather than looking at x as that whole line to the end of the circle.

whitemonsterbunny17 · Answer

So x=9, that makes sense. 
But I don't see what the equation would be to find that.. the book says right below x what it is.. xD

whitemonsterbunny17 · Answer

(My point being... No equation is needed.)