Saturday, July 11, 2015

481: Two Circles and One Square

What is the red area?
The two vertices of the square are the centers of two tangent and congruent circles. If the length of a side is 8√2, what is the area of the red part peeping out?

Here is the real question: Does it matter if the circles are congruent, as long as they're tangent and the centers are at the vertices of the square?

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2 comments:

  1. Dave MarainJuly 11, 2015 at 4:32 PM

    Nice extension, great diagram (Geogebra!) and thanks for the mention! While the area of the square would be constant, (R+r)²/2, the sum of the areas of the quarter-circles would involve the factor R²+r² which isn't constant. Am I missing something?

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  2. CurmudgeonJuly 11, 2015 at 4:53 PM

    Not missing anything. Those parentheses matter.

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