Square Construction...

• Nov 1st 2010, 05:13 PM
MATNTRNG
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?
• Nov 1st 2010, 08:39 PM
Soroban
Hello, MATNTRNG!

Quote:

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?

I would construct the circles first.

. . $\displaystyle \begin{array}{ccc} |\!\! \bigcirc \!\!| \\ \hline \bigcirc\! | \!\!\bigcirc\!\! | \!\bigcirc \\ \hline |\!\! \bigcirc \!\! | \end{array}$

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