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Re: two circles
Posted:
Oct 27, 1994 9:56 AM
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>
> QUESTION:
>
> Consider two non-intersecting, non-congruent circles. What is the locus
> of centers of circles which are tangent to each of these two circles?
>
>
> Monte J. Zerger Voice: (719) 589-7546
> Adams State College FAX: (719) 589-7522
> Alamosa, CO 81102 e-mail: mzerger@cc4.adams.edu
>
>
> staqi@students.wisc.edu gives:
>
> ANSWER:
>
> Draw a line between the centers of the given circles. Consider the
> segment from the end of one circle to the end of the other. The locus
> is the line perpendular to the line between the centers at the midpoint of
> the segment.
>
I don't agree. Define the radii of the given circles to be r and R, and the radius
of the tangent circle to be rho. Then the center of the tangent circle is a
distance R+rho from the center of one of the given circles, and r+rho from the
center of the other given circle. The difference in distance is a constant:
diff = R + rho - (r + rho)
= R - r
Thus the locus of the centers is a hyperbola.
Roger Cappallo
Haystack Observatory
rjc@wells.haystack.edu
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