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Locus of a circle center?
I put this up a couple of weeks ago, but received no correct answers. Can we try again?
Two fixed, intersecting circles have unequal radii. A variable circle is tangent to both of the fixed circles. Describe the locus of the center of the variable circle.
0 Answers
- gianlinoLv 71 decade agoFavorite Answer
The difference of the distances to the centers is | R - R'| . So you get a hyperbola.
One branch corresponds to the varying circle containing both fixed,
The other branch to circles either in the intersection or exterior to both.
The asymptotes are normal to the common tangents and cross at the midle of the centers.
Edit: Btw I forgot an ellipse. This one takes into account the circles which are interior to one of the circles and exterior to the other. This ellipse has same foci as the hyperbola so it is orthogonal to it. They cross at 4 points, 2 of them being the intersection of the circles.
@ Madhukar. Obviously you have something inside the intersection. The circles squeezed in there have their centers just there.
You also have the second branch.
This branch is the center of circles containing both intersecting circles.
Source(s): http://mathworld.wolfram.com/Hyperbola.html