Circular Window

Use compass and ruler to construct the following design of a circular window.

How can it be constructed?


What fraction of the area of the circle is in the "triangular" region in the center bounded by three arcs?






Pose additional problems from this design or from elaborations on it.

Example: Given that the radius of the smaller inscribed circles is a, express the radius r of the larger circle in terms of a.

Other window designs?

For example, a window similar to the following is in one of our local churches:

Compare the relative sizes of the areas in the six regions.


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