graphics - Drawing a quadrilateral inscribed within a circle

I would like to draw a quadrilateral inscribed within a circle. How can I construct this figure, taking into account arbitrary (specified) side lengths, while still ensuring that the vertices of the quadrilateral lie on the circle?

Answer

I hope I understood your question correctly. When you place your figure at {0,0}, meaning the center of the circle and the center of the rectangle is there, you don't need to calculate very much. Indeed, everything is then fixed by exactly one point p defining a corner of the rectangle and the radius of the circle.

A dynamic version of your graphics can be written down in only a few lines of code

Manipulate[
 Graphics[{FaceForm[None], EdgeForm[Thick], Rectangle[-p, p],
   Thick, Red, Circle[{0, 0}, Norm[p]]}, PlotRange -> {{-2, 2}, {-2, 2}}],
 {{p, {1, 1}}, Locator}
]

Mathematica graphics

Comments

plotting - Plot 4D data with color as 4th dimension

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plotting - Filling between two spheres in SphericalPlot3D

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plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....

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