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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 15, 2012 11:53 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.
> In this puzzle is sought a practical construction on an A4 sheet of paper that avoids entirely the use of r1-r2.

Let AA0 be the radius of (A,r1) perpendicular to line AB
Let BB0 be the radius of (B,r2) perpendicular to line AB
From A drop perp AA1 to line A0B0
From B drop perp BB1 to line A0B0
Produce AA1 to meet circle(A,r1) in A12
Produce BB1 to meet circle(B,r2) in B12

Line A12B12 is a close approx to the required tangent.

A second iteration, by dropping perps from A and B to line A12B12 and extending these to A22B22 will be only marginally more accurate for the tangent line, but it will give a slight improvement of the location of the points of tangency.

Regards, Peter Scales.

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