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A circle has a radius of 14. Let AB be a chord of the circle, such that AB = 12. What is the distance between the chord and the center of the circle?

 Jun 20, 2020
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A circle has diameter XY = 28.

Chord AB is perpendicular to XY, has length 12, and intersects XY at point P.

 

By theorem:  AP · PB  =  XP · PY

                           6 · 6  =  x · (28 - x)

                              36  =  28X - x2

             x2 - 28x + 36  =  0

 

Now, use the quadratic formula:  x  =  [ - -28  +/-  sqrt( 282 - 4·1·36 ) ] / (2·1)

           x  =  ( 28 + sqrt(640) ) / 2     or     x  =  ( 28 - sqrt(640) ) / 2 

           x  =  14 + 4sqrt(10)                       x  =  14 - 4sqrt(10)

 

Distance between the chord and the center of the circle:  14 - ( 14 - 4sqrt(10) )  =  4sqrt(10)

 Jun 20, 2020

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