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Line segment JH is tangent to circle G at point J. What is the value of line segment KH?

 Jan 26, 2021
 #1
avatar+116126 
+1

Note that KG  = 5

 

So....we  have a right triangle  such that

 

HJ^2  + GJ^2   =  (GK + HK)^2

 

12^2  +  5^2  = ( 5 + HK)^2

 

144  +  5^2   = 25  + 10 HK  + HK^2

 

169  = 25  +10HK + HK^2

 

144   = 10HK + HK^2

 

HK^2  + 10HK  - 144   =  0

 

(HK - 8)  ( HK + 18)  =  0

 

The first  factor  set to 0  solves this

 

HK  - 8  = 0

 

HK  =  8

 

(We could actually see  that we have a 5-12-13  right triangle....so HK =  13 -  5  =  8)

 

cool cool cool

 Jan 26, 2021
 #2
avatar+1034 
+2

JH = 12          JG = GK = 5

 

KH = sqrt(JG2 + JH2) - GK         

 

KH = 8 units   

 Jan 26, 2021

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