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avatar+102 

https://imgur.com/a/gVGtWMQ

Could you help, the question is about a point of tangency in a circle

 Jun 9, 2021
 #1
avatar+795 
+2

$r^2 + 18^2 = (r+6)^2$

$r^2 + 324 = r^2 + 12r + 36$

$12r = 288$

$\boxed{r = 24}$

 #2
avatar+121048 
+2

POQ  forms  a right triangle with  angle QPO  = 90 degrees     (a tangent always meets a radius at 90° )

 

So....using the Pythagorean Theorem

 

OP^2  = QO^2  -  PQ^2

 

OP^2   = (r + 6)^2 -  18^2

 

r^2  = r^2 + 12r  + 36  - 324

 

12r   =  324  - 36

 

12r  =  288

 

r  = 288  / 12     =   24

 

 

cool cool cool

 Jun 9, 2021

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