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Math Help - Find a radius

  1. #1
    Junior Member
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    Find a radius

    An arch over a door is 60 cm high and 200 cm wide, find the radius of a circle containing the arc of the arch. I have included the picture from my book. The answer should be 113.3333 i believe

    I have set up the problem

    x(60)=100(100) to find the missing part of a chord

    and I tried pythag thm

    I do not know what else to do Thanks for the help
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  2. #2
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    Hello, algebraisabeast!

    An arch over a door is 60 cm high and 200 cm wide.
    Find the radius of a circle containing the arc of the arch.
    Code:
                    C
                  * o *
              *     |     *
          A o - - - o - - - o B
              *     |D    *
                *   |   *R
                  * | *
                    *
                    O

    The radius of the circle is: OA \:=\: OB \:=\: OC \:=\: R

    The width of the arch is: AB \:=\: 200 \quad\Rightarrow\quad AD \:=\: DB \:=\: 100

    The height of the arch is: CD \:=\: 60.
    . . Hence: DO \:=\: R -60


    In right triangle ODB\!:\;\;OD^2 + DB^2 \:=\:OB^2 \quad\Rightarrow\quad (R-60)^2 + 100^2 \:=\:R^2

    So we have: . R^2 - 120R + 3,\!600 + 10,\!000 \:=\:R^2 \quad\Rightarrow\quad 12R \:=\:13,\!600

    Therefore: . R \:=\:\frac{13,\!600}{12} \:=\:\frac{3400}{3} \:=\:1133\tfrac{1}{3} cm.

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