Ellipse Between Two CirclesThe locus of centers of the circles inscribed in an arbelos is an ellipse. Arbelos - a crescent shaped figure - is formed by two tangent circles, one inside the other. Relaxing the tangency condition we obtain what may be called a blunt arbelos - an intermediate shape obtained by morphing an arbelos into an annulus. A third circle can be inscribed into the shape touching the bigger circle internally and the smaller one externally. As with the arbelos, the centers of such circles lie on an ellipse.
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Assuming the two circles have centers on the x-axis, one
Quite clearly the sum of distances of the center O of the inscribed circle to the centers of the two given circles is The minor axis can be found by considering the extreme case of the inscribed circle with the center at the top point of the ellipse. This point along with the centers of
The minor axis of the ellipse is 2h. Conic Sections > Ellipse
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