The Mathematics Education Department
EMT 725, Lisa F. Garey

Circular Window

Click here for Problem statement

Using the hint provided, the GSP construction of this pretty window begins with an equilateral triangle and all its medians.

The figure below shows the auxillary constructions. Have a look at the GSP script for a step-by-step construction.

The area of the "triangular" center can be obtained by subtracting the area of the 3 sectors from the equilateral triangle.

Area(CAB) = 1.39 square inches

Area(Sector) = 0.42 square inches

Radius of large circle = 1.93 inches

Area(Large Circle) = 11.71 square inches

Then, the "triangular" center has area = Area(CAB) ­ 3*Area(Sector) = 0.13 square inches.

Then, of the large circle is the triangular center.

Click here for an active GSP sketch.

Extension:

As an extension, how about another circular window with a different pattern? Instead of "triangular" center, we can have a "square-like" center.

Similar to the original window, the new circular window begins with a square. The figure below shows the auxillary constructions. The GSP script provides a step-by-step construction.

As in the original problem, the "squarish" center has an area a fraction of the large circle.

Then the area of "squarish" center = .

Also, of the large circle is the "squarish" center.

Click here for an active GSP sketch.

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