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Thread: need help in less than 3grs circle

  1. #1
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    need help in less than 3hrs circle

    neefd help fast
    Last edited by AHDDM; Jun 27th 2006 at 03:13 PM.
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  2. #2
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    Hello, AHDDM!


    We are given: $\displaystyle AD = 12$ and $\displaystyle DC - BD = 18\;\;\Rightarrow\;\; DC = BD + 18$


    Let $\displaystyle BD = x$, then $\displaystyle DC = x + 18$

    $\displaystyle \Delta ABC$ is inscribed in a semicircle.
    . . Hence, $\displaystyle \Delta ABC$ is a right triangle.

    $\displaystyle AD$ is the altitude to the hypotenuse of a right triangle.

    Theorem: The altitude to the hypotenuse of a right triangle is
    . . the mean proportional of the two segments of the hypotenuse.

    Hence: .$\displaystyle x(x+18) \,=\,12^2$

    We have the quadratic: .$\displaystyle x^2 + 18x - 144\:=\:0$

    . . which factors: .$\displaystyle (x - 6)(x + 24) \:=\:0$

    . . and has the positive root: .$\displaystyle x = 6$


    Therefore: .$\displaystyle BD = 6,\;\;DC = 24\quad\Rightarrow\quad BC = 30$ cm.
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  3. #3
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    thx 4 the reply

    i keep frogetting to subtitute gotta learn to remeber
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