- #1

Mr.Miyagi

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Suppose I have the following set of equations

[tex]x=3\pi r-r-2\sin\theta[/tex]

[tex]y=r-2\cos\theta[/tex]

[tex]\tan\theta=y/x[/tex]

with r as a constant

How would I go about finding out if an analytical solution exists? There must be a solution, as I distilled the equations from a fairly straightforward geometrical problem that I conjured up.

I just can't seem to find it.

The geometrical problem is basically finding the length of the inner tangent of two circles, between the points where the tangent and the circles touch plus parts of the circles. It's length would be [tex]\sqrt{x^2+y^2}[/tex] and the parts of the circle have a length [tex]2\theta r[/tex]. I hope this makes sense.

[tex]x=3\pi r-r-2\sin\theta[/tex]

[tex]y=r-2\cos\theta[/tex]

[tex]\tan\theta=y/x[/tex]

with r as a constant

How would I go about finding out if an analytical solution exists? There must be a solution, as I distilled the equations from a fairly straightforward geometrical problem that I conjured up.

I just can't seem to find it.

The geometrical problem is basically finding the length of the inner tangent of two circles, between the points where the tangent and the circles touch plus parts of the circles. It's length would be [tex]\sqrt{x^2+y^2}[/tex] and the parts of the circle have a length [tex]2\theta r[/tex]. I hope this makes sense.

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