[Original post lost; I forget the exact question -- djr] ============================================================================== Date: Mon, 18 Dec 1995 15:00:15 +0100 From: desco12@calvanet.calvacom.fr To: rusin@math.niu.edu Subject: maths and land surveying I thank you for your help: *---------------------------------------* For example, the problem you stated is easy in some sense: rotate and translate so that the line is at the origin and so that the circles are of the form (x-h_i)^2+(y-k_i)^2=r_i^2. If the desired circle has radius R and is at the point (x0,y0), then you know (x0,y0) must be of distance R+r_i from the i_th circle, and of distance R to the horizontal axis. This place (x0,y0) on the parabola of points equidistant from the i-th circle and the line y=-r_i. Thus, (x0,y0) can be found by intersecting two parabolas. Writing each in the form y=a_i(x-h_i)^2 + b_i, it is easy to find the point (x0,y0) by solving a quadratic in x0. On the other hand, with ruler and compass alone it is not easy to find the intersection of two parabolas. *----------------------------------------* Now, I just don't know how I could get the parameters of the parabolas (a_i and b_i)? perhaps at the abscissa h_i where y=(k_i-r_i)/2 and y'=0??? Waiting for your answer, Philippe CARRIER