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Let $\overline{AB}$ and $\overline{CD}$ 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 $CQ$.

 

TYSM!!!!

 May 18, 2021
 #1
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Intersecting  Chord Theorem

 

Let   CQ = x    and  DQ =  38  - x

 

We  have  that

 

AQ  * BQ  =  CQ  *  DQ

 

6  * 12   =   x ( 38  - x)

 

72  =  38x  - x^2          rearrange  as

 

x^2  -  38x  +  72   =   0       factor  as

 

(x - 36)  ( x - 2)   =  0

 

Setting each  factor to 0  and solving for  x   we have

 

x = 36     reject

 

x = 2   =  min  length of  CQ

 

 

cool cool cool

 May 18, 2021
 #2
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thank you!!! i rly appreciate it!!!

 May 18, 2021

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