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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.

 Jun 23, 2021
 #1
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Intersecting Chord Theorem

 

AQ  *  QB  =  CQ *  QD

 

6  *  14    =     x  *  ( 38 - x)

 

84   =  38x   -  x^2

 

x^2   -38x  +  84  =  0

 

x =      (  38 -   sqrt  [ 38^2  - 4* 84 ] )  /   2   ≈  2.356  =  min for  CQ

 

 

cool cool cool

 Jun 23, 2021

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