Ellipse Between Two Circles
The 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.

What if applet does not run? 
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Copyright © 19962018 Alexander Bogomolny

What if applet does not run? 
Assuming the two circles have centers on the xaxis, 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
h² = ((r_{1} + r_{2}) / 2)²  ((x_{2}  x_{1}) / 2)². 
The minor axis of the ellipse is 2h.
Activities Contact Front page Contents Geometry
Copyright © 19962018 Alexander Bogomolny