We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
583
2
avatar+166 

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.

 Sep 3, 2017
 #1
avatar+99351 
+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

 Sep 3, 2017
 #2
avatar+21977 
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

 Sep 4, 2017

8 Online Users

avatar