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

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Avni Pllana

Posts: 480
Registered: 12/6/04
Re: Circle-circle tangent puzzle
Posted: Jun 17, 2012 5:24 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.
>
> Best regards,
> Avni


Hi Peter and Mark,

many thanks for the contributions. Peter's solution involves approximations and iterations, therefore not very practical.
Mark's solution is correct and the sought one. The basic idea was to make use of the radical line of two circles. It is well-known that radical lines of any three circles are concurrent. This menas we can use an arbitrary circle that intersects C1(A,r1) and C2(B,r2) to construct their radical line. Mark used a specific one C3(D,r3). Very nice.

Best regards,
Avni



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