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Topic: Circle-circle tangent puzzle
Replies: 5   Last Post: Jun 17, 2012 5:24 AM

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Peter Scales

Posts: 192
From: Australia
Registered: 4/3/05
Re: Circle-circle tangent puzzle
Posted: Jun 6, 2012 9:22 AM
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> 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

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