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Let AB and CD be chords of a circle, that meet at point Q inside the circle. If AQ=6 ,BQ=12 and CD=38, then find the minimum length of CQ.

 Apr 12, 2021
 #1
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AQ * BQ  =  CQ  *  DQ

 

6  *  12   =  x *  (38 - x)

 

72  =  38x  -  x^2               rearrange  as

 

x^2   -  38x  +  72   =   0      factor

 

(x - 36)  ( x - 2)   =   0

 

The  second factor set  to 0  and solved  for  x  gives  the  minimum  length of CQ

 

x  - 2  = 0

 

x  = 2  =  CQ

 

cool cool cool

 Apr 12, 2021

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