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I have a small problem I've been trying to resolve for the last hours but with not succes. I have two circles in R^2, for each one I know it's center and radius = 1.

I have a point somewhere in R^2. How can I figure out if that point is in the convex hull of the two circles or not? Thank you.

Ciprian Trinca
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  • find the distance between the point and the two centers and check if atleast one of them is less than $1$ ? – sciona Nov 30 '14 at 11:28
  • The convex hull is an oval like that: http://goo.gl/qpwAeO Testing whether some point is inside or outside will require a nasty case analysis. Informally, I would phrase it like "x inside circle 1" or "x inside circle 2" or "x inside rectangular" (those three are not mutually exclusive). – GDumphart Nov 30 '14 at 11:28
  • @sciona I disagree, there are points inside the convex hull farther than 1 away from any center. – GDumphart Nov 30 '14 at 11:29
  • @GDumphart ah ! so the region bounded between the pair of circles and their direct common tangents as well ! thanks for clearing it :-) – sciona Nov 30 '14 at 11:31
  • well drawing a vertical line $l_p$ through the point $P$(say) to the line joining the centers $l_0$, finding the points of intersection of the line $l_p$ with the pair of direct common tangent lines $t_1,t_2$ at points $P_1,P_2$ respectively and checking if $P = \lambda P_1 + (1-\lambda) P_2$, for a $1 \ge \lambda \ge 0$ should verify the remaining case .. – sciona Nov 30 '14 at 11:41

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