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Circles A and B are externally tangent.  Angle PAB is a right angle.  Segment PT is tangent to circle B at T.  If the radius of circle A is 1 cm and the radius of circle B is 4 cm, what is the length of segment PT in cm?

 

 Jul 4, 2022
 #1
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Draw PB

 

Triangle PAB is right with   AB = 5 and PA  = 1    and PB the hypotenuse

 

So

 

sqrt [AB^2  + PA^2 ]   =  PB

 

sqrt [  5^2 +  1^2 ] =  PB

 

sqrt [26] = PB

 

And PBT is also a right triangle with PTB a right angle  and TB = 4 and PB = sqrt (26) and PT a leg

 

So

 

sqrt  [ PB^2  -   TB^2  ]  =  PT

 

sqrt [ 26  - 4^2 ]   =  PT

 

sqrt [ 26 -16 ]  = PT

 

sqrt [ 10 ] (cm) = PT

 

cool cool cool

 Jul 4, 2022

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