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copied!<p>I suppose this question should migrate to a more math related site.</p> <p>Try to imagine where these two tangent circles go when the circles <strong>a</strong> and <strong>b</strong> get further and further apart. They get closer to the line <strong>AB</strong>. Once the <strong>AB</strong> segment equals <strong>4r</strong> these two tangent circles will overlap. From now on, once circles <strong>a</strong> and <strong>b</strong> get further apart, there's no tangent circles whatsoever.</p> <p>If you want to calculate the position of these circles, just assume that the distance between the centers is always <strong>2r</strong>:</p> <p><img src="https://latex.codecogs.com/gif.latex?%28x_C-x_A%29%5E2+%28y_C-y_A%29%5E2%3D4r%5E2%5C%5C%20%28x_C-x_B%29%5E2+%28y_C-y_B%29%5E2%3D4r%5E2" alt=""></p> <p>You should get two, one or none solutions for xC and yC, which will be the centers of your tangent circles. I hope I haven't messed something up.</p> <h2>Solutions</h2> <p>Provided you do know there are solutions ( just check if <code>d(A,B) <= 4r</code> ), these are the coordinates of your two circles:</p> <p><a href="http://pastebin.com/LeW7Ws98" rel="nofollow noreferrer">http://pastebin.com/LeW7Ws98</a></p> <p>A little scary, eh? But it's working. There are the following variables:</p> <p><code>x_A, y_A</code> - the coordinates of the circle A,</p> <p><code>x_B, y_B</code> - the coordinates of the circle B, </p> <p><code>r</code> - the radius. </p> <p>I've checked the solutions with the values from one of my comments below. I think that you can copy these solutions and inject them into your code straight away (provided there's a sqrt function) and get the results after declaring some variables.</p> <p>These solutions are loosely derived from the Save's proposition but I couldn't comment below his answer - I've got less than 50 reputation points, duh ... ( thanks SO! You're the man! ). However I'm pretty sure they should be valid for my system anyways. Cheers</p>

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