TITLE: How to test if a point is inside the convex hull of two circles?
QUESTION [6 upvotes]: Following my previous question, I'm wondering how I can determine if a point is within the convex hull of two circles (a boolean value). There's no problem testing if the point is in either of the two circles, but it can also be "between" them and I don't know how to test for that.
Seeing Wolfram MathWorld's article on Circle-Circle Tangeants, it seems that an inequation that tests if the point is on the internal side the two external circle tangeants would do the trick, but I'm afraid my solving skills are too far away to be able to turn the tangeant equations into a fitting inequality.
I'm defining the convex hull of two circles using both centers and radii.

REPLY [7 votes]: You can first calculate the four points of tangency, then use the Point in Polygon algorithm to determine if your point is inside the quadrilateral (this is assuming you have a programming related problem)
Otherwise, once you have found the four tangent points, you can form four lines and get four simultaneous inequalities.