SOLUTION: the center of a circle is at (4,2) and its radius is 5. find the length of the chord which is bisected at (2,-1).

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Question 1084921: the center of a circle is at (4,2) and its radius is 5. find the length of the chord which is bisected at (2,-1).
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Determine the slope of the line from (4,2) to (2,-1).

Now determine the slope of the bisector since they're perpendicular,



Determine the equation of the line using the point and the slope,



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Now find the intersection of that line with the circle.












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So then,

Finally calculate the distance from the two intersection points using the distance formula, that's the length of the chord.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
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the center of a circle is at (4,2) and its radius is 5. find the length of the chord which is bisected at (2,-1).
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Below I placed much simpler solution. 

1.  Make a sketch to follow my arguments.

    Let the point O = (4,2) be the center of the circle,
    and let the point A = (2,-1) bisects our chord.

    Let B  and C be the endpoints of the chord.


2.  Then  =  + ,   or

    For |OC| you have   = 25  and  for  |OA| you have 

      =  =  = .


    Therefore,   =  = 12.

    Then |AC| =  = ,

         and  |BC| = .

Answer. The length of the chord is .



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