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Mathematics-Online problems:

Problem of the week

Let $ ABCD$ be a square with side length $ r=1$.
\includegraphics{A980_bild1}

In the figure above, determine the angle $ \widehat{PAQ}$, the length of the line segment $ \overline{PQ}$, and the area $ A$ of the intersection of the four quarter-circles (shaded region).


Answer:

$ \widehat{PAQ}$ (in degrees) =
Length of $ \overline{PQ}$ =
Area $ A$ =

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


   

[solution to the problem of the previous week]