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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 = 14, and CD = 38, then find the minimum length of CQ.

 Mar 31, 2022
 #1
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We  have that

 

AQ * BQ   =  CQ * DQ

 

Let CQ = x   and  DQ =  38 - x

 

So

 

6 * 14  =  x * (38 - x)

 

84  = 38x - x^2                  reararrange   as

 

x^2 - 38x + 84  = 0            

 

Using the Quadratic Formula   the  minimum for x = CQ  ≈  2.3567

 

 

cool cool cool

 Mar 31, 2022

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