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Mathematics-Online problems:

Interactive Problem 60: Circles in a Circle

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#./interaufg60_en.tex#As you can see from the figure below, $ n$ circles with radius $ r$ are inscribed in a circle with radius $ 1$.

\includegraphics{A755_vier_kreise}     \includegraphics{A755_drei_kreise}

Determine the radius $ r$ and the area $ A$ of the shaded region between the circles for $ n = 4$ and $ n = 3$.

Hint: In an equilateral triangle the medians divide each other in the ratio of $ 2 : 1$.


Answer:

$ n = 4$:     $ r=$ $ ,$    $ A=$
$ n = 3$:     $ r=$ $ ,$    $ A=$

(The results should be correct to four decimal places.)


   

(From: Day of Mathematics 1995)
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  automatically generated: 2/ 6/2018