> > Let A, B be the centers of two circles with radius > > r1, r2 respectively, where r1-r2 is very small. > > Construct the exterior tangent to the given > circles. > > > Draw circles C1(A,r1) and C2(B,r2) > Draw circle C3(A,r1-r2) > Draw circle C4 on AB as diameter > > Then C3 and C4 meet in P with BP perpendicular to AP > Produce AP to meet C1 in T1 > Draw BT2 // AT1 to meet C2 in T2 > > Then T1T2 is the required common tangent. > > If r1-r2 (=d) is considered too small for this > construction to succeed, then proceed as follows: > > Let angleABP =alpha > then sin(alpha)=d/AB=D/r1 > > Therefore D=d.r1/AB > > Draw a line perpendicular to AB at distance D from A > towards B > This line meets C1 at T1, since D subtends alpha at A > > > > Regards, Peter Scales. > > > Message was edited by: Peter Scales on 6 June 2012
your solution is correct and it is well-known, but it still uses the length d = r1-r2 . In practical constructions on an A4 sheet of paper the small r1-r2 causes difficulties and results are not satisfactory. In this puzzle is sought a solution that avoids entirely the use of r1-r2.