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Two distinct points $A$ and $B$ are on a circle with center at $O$, and point $P$ is outside the circle such that $\overline{PA}$ and $\overline{PB}$ are tangent to the circle. Find $AB$ if $PA = 12$ and the radius of the circle is 9.

AdminMod2  Sep 3, 2017
 #1
avatar+87301 
+1

 

OA is a radius = 9

 

Because  OAP  is a right angle, OP  = sqrt ( PA^2 + OA^2)  = sqrt (12^2 + 9^2)  = 

sqrt (225)  =  15

 

Let AB intersect OP at R

 

And triangles  OPA and OAR  are similar

 

So

 

PA / OP  =  AR / OA

 

12 / 15  =  AR / 9

 

AR  = 108/15  =  36/5

 

And AR  = (1/2) AB  ...so

 

AB  = 2 (AR) =  2(36/5)   =  72/5

 

 

cool cool cool

CPhill  Sep 3, 2017
 #2
avatar+19649 
0

Two distinct points $A$ and $B$ are on a circle with center at $O$, and point $P$ is outside the circle such that $\overline{PA}$ and $\overline{PB}$ are tangent to the circle. Find $AB$ if $PA = 12$ and the radius of the circle is 9.

 

see: https://web2.0calc.com/questions/circle-tangent

 

laugh

heureka  Sep 4, 2017

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