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Math Help - [SOLVED] semi-circle

  1. #1
    dnoster
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    [SOLVED] semi-circle

    hi everyone
    please could someone help me with a problem. If i have a semi-circle, and at the baseline , at certain intervals on that baseline, i need to know what the height is to the arc of the semi-circle , at right angles to the baseline , would anyone have a formula i could use

    cheers
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  2. #2
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    Hello, dnoster!

    I have a semicircle, and at certain intervals on the diameter, I have points.
    I need to know the height from the points to the arc of the semicircle.
    Code:
              C
              * * *
            */: \     *
          * / :   \     *
         * /  :     \    *
          /   :h      \
        */    :         \ *
        *-----*--+--------*
        A  x  P   2r-x    B
    A triangle inscribed in a semicircle is a right triangle: . \angle C = 90^o

    We have a point P on the diameter, where AP = x.

    If r is the radius of the circle, then PB = 2r - x


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


    That is: . h^2 \:=\:x(2r-x)

    Therefore: . h\:=\:\sqrt{x(2r-x)}
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  3. #3
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    Quote Originally Posted by dnoster
    hi everyone
    please could someone help me with a problem. If i have a semi-circle, and at the baseline , at certain intervals on that baseline, i need to know what the height is to the arc of the semi-circle , at right angles to the baseline , would anyone have a formula i could use cheers
    Hello,

    here is another way to do your problem:
    Let the center of your circle be the origin of a coordinate system. Then you can use the Pythagorian theorem:

    x-value = b
    height to the arc of the semi-circle = a

    Then you get:

    a^2+b^2=r^2\ \Longrightarrow \ a=\sqrt{r^2-b^2}

    I've attached a diagram to show what I've calculated.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails [SOLVED] semi-circle-krs_punkt1.gif  
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