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Re: Circle-circle tangent puzzle
Posted:
Jun 6, 2012 12:58 PM
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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
Hi Peter,
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.
Best regards,
Avni
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