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Math Help - Circumscribe a square about a semicircle!

  1. #1
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    Circumscribe a square about a semicircle!

    Thanks!
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  2. #2
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    Re: Circumscribe a square about a semicircle!

    Hello, Jammix!

    Is there any more information?
    I suspect that I know the solution . . . but it's only a guess.


    Circumscribe a square about a semicircle.

    Code:
                    R
        B * - -.-.*.o.*.-.- * C
          |  .*:::::|:::::*.|
          | *:::::::|:::::::o S
          |*::::::::|:::::* |
          |:::::::::|:::* r |
          *:::::::::|:*     *
        Q o:-:-:-:-:O - - - o
          *:::::::* :       *
          |:::::*r  :       |
          | ::*     :       |
        A * o - - - * - - - * D
            P       E
    Square ABCD is circumscribed about the (tilted) semicircle.
    The circle has center O and radius r\!:\;OP = OQ = OR = OS = r.

    \Delta OEA is an isosceles right triangle.
    Hypotenuse PO = r \quad\Rightarrow\quad OE = \tfrac{\sqrt{2}}{2}r

    Let x = AB, the side of the square.

    Then: . x \:=\:RO + OE \:=\:r + \tfrac{\sqrt{2}}{2}r

    Therefore: . x \:=\:\left(\tfrac{2 + \sqrt{2}}{2}\right)r
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  3. #3
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    Re: Circumscribe a square about a semicircle!

    Can you give me the steps in which you constructed that? Thanks!
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  4. #4
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    Re: Circumscribe a square about a semicircle!


    Correction: . \Delta OE\color{red}{P} is an isosceles right triangle.


    (I was not allowed to edit my post. Why?)
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