> 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
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