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Math Help - Finding Chords secants and tangents...

  1. #1
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    Finding Chords secants and tangents...

    Hey could someone help me solve this one:

    "A bridge over a river has the shape of a circular arc. The span of the bridge is 24 meters. The midpoint of the arc is 4 meters higher than the endpoints. What is the radius of the circle that contains this arc?

    Thanks
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  2. #2
    Eater of Worlds
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    There are various ways, but you could try.

    (r-4)^{2}+12^{2}=r^{2} and solve for r.
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  3. #3
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    so..

    so wanted to make sure I simplified right...r squared plus 16 plus 144 equals r squared?
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  4. #4
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    Hello, zachcumer!

    so wanted to make sure I simplified right...
    r squared plus 16 plus 144 equals r squared? . . . . no
    Don't do that!

    (r-4)^2 \;=\;(r-4)(r-4) \;=\;r^2 - 4r - 4r + 16 \;=\;r^2 - 8r + 16

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  5. #5
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    The final part is

    r^2-8r+16+144= r^2

    So "R" equals 20!

    right?
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  6. #6
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    Yes, r = 20. Good!.
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