Square with 2 quarter circles. Square has sides 4 and the circles go from 1 top corner to the opposite bottom corner. The two quarter circles intersect in the middle, and a shape is left at the top. I need the perimeter of that shape. Thanks.
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1You've gotta describe it more clearly, or provide a diagram. – Andrew Chin Mar 16 '20 at 18:18
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One way to describe it more clearly would be to give names to the points. For example, if the square is $ABCD$, am I correct that one circle has center $C$ and radius $BC$, while the other circle has center $D$ and radius $AD$? If we let $M$ be the point inside the square where the two circles meet, and we let $X$ be the shape that you want the perimeter of, then is $X$ the shape that's bounded by line segment $AB$ and circular arcs $AM$ and $BM$? – user729424 Mar 16 '20 at 18:30
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Well, though it is not very clear from the question but making few assumptions, I think you are looking for this.
The triangle formed by the point of intersection of the quadrants and the bottom corners is an equilateral triangle. Now, for the first quadrant angle opp to $l_1$ is $\frac{\pi}{6}$ and thus $l_1=\frac{R\pi}{6}$.
Mathsmerizing
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