PROBLEM: 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 the three arcs?


Discussion/Solution?:


Construct the circular window:
Now let's turn our attention to the "triangular" region in the center.

We want to determine the fraction of the area of the original circle that that is covered by the "triangular" region bounded by the three arcs.


Let r = the radius of the original circle.
Let 2x = the side of the triangle joining the centers of the incsribed circle
So x = the radius of an inscribed circle


Relate x to r ----





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