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Let's say I have a triangle (just a basic equilateral). What I'd like to do is render it by specifying its radius and center, and then calculate the vertices from there.

What is the formula for this? This object will not be static, as I will be altering its position multiple times.


I should also note that this is on a Cartesian coordinate system.

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In the complex plane, its vertices should be $C+R.e^{\iota(\theta+2\pi k/3)}=(x_c+R\cos(\theta+2\pi k/3),y_c+R\sin(\theta+2\pi k/3))$ for $k=0,1,2.$ – Giuseppe May 26 '12 at 22:55
Is C and R Matrices or vectors? – about blank May 27 '12 at 1:49
$R$ is your radius and $C=(x_c,y_c)$ is your center. – Giuseppe May 27 '12 at 7:04

Well, since in an equilateral triangle angle bisectors, medians, altitudes, perpendicular bisectors are all the same, the circumcenter and incenter (and orthocenter) are the same point, what I guess you call "the triangle's center". Now, by "triangle's radius" I'm guessing you mean the triangle's circumcircle's radius, and then: you need three point on the plane such that

i) They're equidistant from the circumcenter, and

ii) This common distance is 2/3 of each median's length.

Of course, you'll get infinite possibilities as any such solution can be rotated around the circumcenter in any angle $\,0<\theta<2\pi /3 $ and you'll get a new set of three vertices of an equilateral triangle with the same circumcenter.

If my guessing of your naming is incorrect then discard the above.

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