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Math Help - Square Construction...

  1. #1
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    Square Construction...

    The given figure is a square with side measure a. The inner quadrilateral is also a square. Congruent circles are inscribed in each triangle and in the inner square. Find the radius of the circle in terms of a. How would you go about making this construction?
    Square Construction...-square.jpg
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  2. #2
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    Hello, MATNTRNG!

    The given figure is a square with side measure a.
    The inner quadrilateral is also a square.
    Congruent circles are inscribed in each triangle and in the inner square.
    Find the radius of the circle in terms of a.
    How would you go about making this construction?
    Click image for larger version. 

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    I would construct the circles first.

    . . \begin{array}{ccc}<br />
|\!\! \bigcirc \!\!| \\ \hline<br />
\bigcirc\! | \!\!\bigcirc\!\! | \!\bigcirc \\ \hline<br />
|\!\! \bigcirc \!\! |<br />
\end{array}


    Then add the tangent lines.

    . . \begin{array}{ccc}<br />
\bigg \wedge \\[-3mm]<br />
/\! \bigcirc \!\backslash \\ <br />
\langle \bigcirc \!\! \bigcirc \!\! \bigcirc \rangle  \\ <br />
\backslash\! \bigcirc \!/ \\[-3mm]<br />
\bigg \vee<br />
\end{array}
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