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In the figure, $AP$ is tangent to the circle centered at $O$, $AB=BC,$ and $AP=3\sqrt{2}$. Find the length of $AC$.

 

 Feb 5, 2021
 #1
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3sqrt (2)   =  sqrt (18)

 

Using  the  secant tangent theorem

 

AP^2   = AB  ( AB + BC)

 

Since  AB  =BC   then  let them  =  x

 

AP^2  =  x  ( x + x)

 

(sqrt 18)^2   =  x (2x)

 

18  = 2x^2     divide both sides  by 2

 

9 = x^2

 

3  = x

 

So

 

AC  = 2x   = 2 (3)    =  6

 

cool cool cool

 Feb 5, 2021

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