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Seems like this is a simple question, but my own created equations don't seem to replicate results for other combinations of circles.

Circle A at (0,0) has a radius of 6.
Circle B at (15,0) has a radius of 2.

Continuing this trend, what is the radius of a Circle C at (Cx, 0) and can this be generalized to fit other Circle A and B combinations (where Circle A is always the largest)?

Edit: The further away from Circle A, the smaller the radius will be. The regression will be linear (and consequently the radius will eventually hit zero). For a similar image that could illustrate what I mean, you might say Circle A is a lightsource, Circle B is an object smaller than the lightsource, and Circle C is a shadow.

Thanks for your time!

user3023925
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1 Answers1

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You can certainly fit a line through $(0,6)$ and $(15,2)$ to say a circle with center at $(C,0)$ should have a radius of $6-\frac 4{15}C$. If $C \gt \frac {45}2$, the radius goes negative. You could also fit curves like a falling exponential so the radius is always positive.

" can this be generalized to fit other Circle A and B combinations (where Circle A is always the largest)"? Of course. The question is so vague that it is not clear what you are looking for.

Ross Millikan
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  • Ok, I edited my question. Hopefully it is more clear. Where I'm getting stuck is expressing this is terms of variables for similar combinations. – user3023925 Sep 05 '15 at 23:36
  • With the edit, you can do just what I suggested. Put a line through the two points (0, radius at 0), (distance from A to B, radius at B). That gives you the radius at any distance from A. Look up the two point form of a line to see how I got it. – Ross Millikan Sep 05 '15 at 23:43