Circle through two points & tangent to an arc.

 From: blowlamp 30 Oct 2012  (1 of 17)
 Hi Michael. In this video I'm running the v3 beta and attempting to draw a circle which passes through the centre of the two large black circles and makes a tangent with the smaller green one too. I also try something similar with the red line, but notice how Tan (and Perp) is displayed in what I think is the wrong position over the green circle - these snap points seem to be rotated anti-clockwise a number of degrees from their proper position, unless I'm misunderstanding something about what they should be indicating to me. http://screencast.com/t/8yGlS9fQy Cheers. Martin (2).

 From: Frenchy Pilou (PILOU) 30 Oct 2012  (2 of 17)
 5513.2 In reply to 5513.1 Rotate the circles A , B around the circle O by the center O untill have line AB perpendicular to the vertical line OM (M is middle of AB) You can now Draw your Circle by the 3 points ABC tangent in C! (C = Intersection OM and arc) Make the rotation inverse if necessary for have the start position :) EDITED: 30 Oct 2012 by PILOU

 From: bemfarmer 30 Oct 2012  (3 of 17)
 5513.3 In reply to 5513.2 Here is a method, which I have not studied yet: http://math.stackexchange.com/questions/32386/finding-the-circles-passing-through-two-points-and-touching-a-circle?rq=1 Also attached a .3dm of the problem, from a screen image trace. Attachments:

 From: blowlamp 30 Oct 2012  (4 of 17)
 Thanks for the replies chaps. Did you notice the Tan and Perp snaps that appeared, but didn't seem to be in the right place to make a useful intersection? Frenchy Pilou. I'm looking at your method, but the penny hasn't dropped with me just yet :) bemfarmer. Thanks for adding the .3dm file. Martin (2).

 From: bemfarmer 30 Oct 2012  (5 of 17)
 I'll probably look at it again tonight, after work, unless someone else solves it.

 From: Michael Gibson 30 Oct 2012  (6 of 17)
 5513.6 In reply to 5513.1 Hi Martin, so the "tan" and "perp" snaps that you are seeing are line-based snaps, when you see them pop up they are showing you a tangent location on a line coming from the previous picked point which in your case here is the second picked point of the arc, not showing you the type of tangency that you're looking for which is more of an "full object" tangency. That type of tangency is usually created by the Circle or Arc tangent command, and not by "Circle through 3 points", but circle and arc tangent are set up to make stuff tangent to 2 curves and through a point, or tangent to 2 curves with a specified radius, or tangent to 3 curves, but not tangent to one curve and through 2 points like you want to do here. Pilou, I think your method will only work in the special case where the 2 points are equal distances away from the center line... It looks like the link bemfarmer posted above has the answer in it, though. - Michael

 From: Frenchy Pilou (PILOU) 30 Oct 2012  (7 of 17)
 5513.7 In reply to 5513.6 << the special case where the 2 points are equal distances away from the center line... There is always only one line between the 2 "upper circles" centers, so an only one middle, so always an only "special position" ;) Try my method, it's a simple simplicity against the theory :) EDITED: 30 Oct 2012 by PILOU

 From: Michael Gibson 30 Oct 2012  (8 of 17)
 5513.8 In reply to 5513.7 Hi Pilou, how would your method work with points like this: - Michael Attachments:

 From: Frenchy Pilou (PILOU) 30 Oct 2012  (9 of 17)
 5513.9 In reply to 5513.8 So simple and works with any 2 points, circles... And when you have drawn your circle 3 Points as I said just rotate as inverse :) EDITED: 30 Oct 2012 by PILOU

 From: Michael Gibson 30 Oct 2012  (10 of 17)
 5513.10 In reply to 5513.9 Hi Pilou, again you seem to be assuming that always the 2 points are equally spaced from one another. Here I will exaggerate it a bit more, try with this example and with the attached file: It is indeed simple if the 2 points are exactly balanced and form an isosceles triangle with the center of the circle as you keep showing, but that's just one special arrangement of points. - Michael Attachments:

 From: Frenchy Pilou (PILOU) 30 Oct 2012  (11 of 17)
 5513.11 In reply to 5513.10 This special case asks some reflexion! :) --- Pilou Is beautiful that please without concept! My Gallery

 From: Michael Gibson 30 Oct 2012  (12 of 17)
 5513.12 In reply to 5513.11 Hi Pilou, the one that you are showing the solution for is the special case with points arranged in a particular configuration. I don't believe that your solution works for the more general case where the points are placed anywhere... - Michael

 From: blowlamp 30 Oct 2012  (13 of 17)
 Well here's my solution http://screencast.com/t/EngogKiRXu6C I don't know if it's the same as the way shown in bemfarmer's link, as that was hard for me to follow, but somehow I got to work it out OK. Martin (2)

 From: Michael Gibson 30 Oct 2012  (14 of 17)
 5513.14 In reply to 5513.13 Hi Martin, I'm glad that you got it solved. I will look into adding this case into the circle and arc tangent commands. - Michael