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From: "Denis B. Roegel" <Denis.Roegel@loria.fr>
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Subject: Re: A little Metapost problem.
Date: Wed, 28 Mar 2001 22:38:18 +0200 (MET DST)
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`David Arnold' wrote
>   
>   Hans, et al,
>   
>   Attached is a little doc. At the bottom of the page, I've attempted to draw
>   to circles tangent to one another. The line PQ is supposed to be a common
>   tangent line, that is, it is supposed to be tangent to both circles. 
>   
>   I used the formula to compute theta, but the asin routine in Metapost is
>   not that accurate and the line dips a little too low on the first circle,
>   and a little high on the second circle.
>   
>   I'd love to see some Metapost experts demo some cute ways of calculating
>   the common tangent PQ. Eventually, when I provide answers for my students,
>   I will need to know that points A and B where the common tangent touches
>   the two circles, as I will need to draw in radii of the circles
>   perpendicular to the common tangent to explain how to do the problem.

Maybe the following is useful?

Denis

beginfig(1);
pair A,B,O,P,Q;
numeric u,r,R;
R=2cm;
r=1cm;
A=origin;
B-A=(5cm,0);
draw fullcircle scaled 2R shifted A;
draw fullcircle scaled 2r shifted B;
O=(1+r/(R-r))[A,B];
P-A=R*(R/arclength(A--O),sqrt(1-(R/arclength(A--O))**2));
Q=(arclength(O--B)/arclength(O--A))[O,P];
draw Q--P--A--B--Q--O--B;
label.rt(btex $O$ etex,O);
label.bot(btex $A$ etex,A);
label.bot(btex $B$ etex,B);
label.top(btex $P$ etex,P);
label.top(btex $Q$ etex,Q);
endfig;
end