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Math Help - Circles! :D

  1. #1
    Junior Member
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    Circles! :D

    I wonder how quick you can work this out...


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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, Geometor!

    PQ and RS are parallel chords 6 cm apart.
    PQ = 10 cm and RS = 14 cm.

    (a) What is the shortest distance from the center to chord PQ?

    (b) Find the radius of the circle.
    Code:
                  * * *
              *  5  T  5  *
           P* - - - * - - - *Q
           *        |        *
                    | x
          *         |         *
          *         *O        *
          *         |         *
                    | 6-x
          R*- - - - * - - - -*S
            *   7   U   7   *
              *           *
                  * * *

    Draw diameter TU through center O, perpendicular to PQ and RS.
    . . Then: .TQ = 5, US = 7.
    Draw radii OP = OQ = OR = OS = r.
    Let x = TO, then 6 - x = OU.

    In right triangle ORQ: .x + 5 .= .r .[1]

    In right triangle OUS: .(6-x) + 7 .= .r .[2]

    Equate [1] and [2]: .x + 25 .= .36 - 12x + x + 49 . . 12x .= .60

    Therefore: .(a) .x = 5

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _
    Substitute into [1]: .5 + 5 .= .r . . . . (b) .r = 5√2

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  3. #3
    Junior Member
    Joined
    May 2007
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    alright, I see. Thanks!
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