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?
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$\begingroup$ It is to be quad in a circle with a user-specified length of the side of a quad, is to change the circle to fit a quad in a circle. $\endgroup$– user5955Feb 18, 2013 at 13:12
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$\begingroup$ Just that, given the length of the side of the square will fit within a circle, which is automatically size to fit the square. $\endgroup$– user5955Feb 18, 2013 at 13:21
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$\begingroup$ I have edited your question according to what I think it means. Can you confirm whether or not this is correct? $\endgroup$– Oleksandr R.Feb 18, 2013 at 13:24
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3$\begingroup$ Perhaps mathworld.wolfram.com/CyclicQuadrilateral.html ? $\endgroup$– cormullionFeb 18, 2013 at 13:37
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2$\begingroup$ @user5955 You image showed a rectangular inscribed. Therefore, I assumed you don't need an arbitrary quadrilateral. $\endgroup$– halirutan ♦Feb 18, 2013 at 13:52
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1 Answer
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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}
]
answered Feb 18, 2013 at 13:49