Apollonius Problem

Hi there, I'm trying to draw a special case of the problem of Apollonius (exactly this one, requires Java to see fully, [THIS IS NOT SPAM, I NEED TO POST THIS LINK]whistleralley(*dot*)com/java/2c0l1p(*dot*)htm)... in my case, I'm trying to draw the four solutions that the problem "draw a circle tangent to two given circles and passes through a given point". AutoCAD correctly draws some of them with Circle->3 points, I use refent mode TANgent, click near the approximate tangent of a solution, click in the given POINT and click near the approximate tangent of the second given circle. It correctly draws some of them, but it's impossible to make it draw all of them, even if I almost use the TANGENT mode in the exact point of tangency of the solution. What can I do?

Which circle were you having trouble with?

I have drawn all four, by using your method and taking the three points in an anti-clockwise direction each time.

OK got it now but this is TRICKY you have to try entering the points at different orders until you get the circle that you want, lol

BTW: does anyone know how to do this manually? I mean, with auxiliary lines, circles and so.

jatepola, I just looked at the Wikipedia entry on this subject and it appears that geometers and mathematicians have been puzzling this out for 2000 years. Years ago I remember solving the special case where three circles are tangent with some simple trig, but now I can't remember how it was done. According to the article, it is possible to solve the problem by compass and straightedge, but I don't know how difficult it is. Check out the article. Solutions have been worked out for spherical generalizations of the problem. Interesting.