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Mathematics-Online problems:

Interactive Problem 64: Intersection of four Quarter-circles

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
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.)


   

(From: Day of Mathematics 1997)
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  automatically generated: 2/ 6/2018