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Math Help - 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; June 27th 2006 at 04:13 PM.
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  2. #2
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    Hello, AHDDM!


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


    Let BD = x, then DC = x + 18

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

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

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

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

    . . and has the positive root: . x = 6


    Therefore: . 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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