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## Constant angle graph [closed]

Given two points A and B in a plane with distance $2r$, let there be a third point C in the same plane, denote the angle ACB by $\alpha$. If $\alpha = \pi /2$, we know the graph of C will be a circle with radius $r$, what if we fix $\alpha$ at some angle other than $\pi/2$? What if points A, B, and C are in 3-D space?

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 The set consists of two circle arcs, but it is surely not appropriate forum. – Fedor Petrov Dec 12 2010 at 10:08 Thank you. You are so helpful. – kindlychung Dec 12 2010 at 10:11