[Original post lost; I forget the exact question -- djr]
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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