Answer to Question #165432 in Analytic Geometry for Ap

Question

Chanelle is creating a design for vinyl flooring.

She uses circles and squares to create the design shown.

If the equation of the small circle is x2 + y2 = 16, what are the dimensions of the large square?

Ok, so, in the cartesian plane, the order of the shapes is as follows:

small circle

small square

larger circle

larger square

Answer 1

$\displaystyle \textsf{Radius of small circle}:\,\,\, 4\,\,\textsf{units} \\ \textsf{Length of smaller square}:\,\,\, 4 + 4 = 8 \,\,\textsf{units} \\ \textsf{Diagonal of smaller square}: \\8^2 + 8^2 = D^2 \hspace{1cm} (\textsf{Pythagoras}) \\ D = 8\sqrt{2}\,\,\textsf{units} \\ \textsf{Diameter of larger square}: 8\sqrt{2}\,\,\textsf{units}\\ \textsf{Radius of larger square}: 4\sqrt{2}\,\,\textsf{units}\\ \therefore\textsf{Length of larger square}:\,\,\, 4\sqrt{2} + 4\sqrt{2} = 8\sqrt{2}\,\,\textsf{units}$