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Math Help - Circle and Chord

  1. #1
    Senior Member DivideBy0's Avatar
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    Circle and Chord

    In a circle of radius 10cm, a chord is drawn 6cm from the centre. If a chord half the length of the original chord were drawn, its distance, in centimetres, from the centre would be

    (A) sqrt(96) (B) sqrt(84) (C) 9 (D) 8 (E) 3pi

    I'm not so familiar with the properties of chords in circles, so please don't explain too fast, thanks.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, DivideBy0!

    In a circle of radius 10cm, a chord is drawn 6cm from the centre.
    If a chord half the length of the original chord were drawn,
    its distance, in centimetres, from the centre would be:

    . . (A) sqrt(96) . . (B) sqrt(84) . . (C) 9 . . (D) 8 . . (E) 3pi
    Code:
                  * * *
              *           *
            *               *
           *                 *
    
          *         O         *
          *         *         *
          *       / | \       *
                /   |6  \ 10
           *  /     |     \  *
           A* - - - + - - - *B
              *     C  8  *
                  * * *
    In circle O with radius OA = OB = 10, chord AB is drawn; OC = 6.

    Using Pythagorus on right triangle OCB, we find that: CB = 8
    . . Hence: AB = 16.


    If we have a chord only 8 units long, it looks like this:
    Code:
                  * * *
              *           *
            *               *
           *                 *
    
          *         O         *
          *         *         *
          *       / | \       *
                /   |d  \ 10
           *  /     |     \  *
           P* - - - + - - - *Q
              *  4  R  4  *
                  * * *
    In right triangle ORQ, we have: .d + 4 .= .10 . . d .= .84

    Therefore: .d .= .√84

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