1) Construct a band of successively tangent circles, which are also tangent to two parallels e1, e2, through B and C.

2) Invert this band, with respect to the circle c, with center A and orthogonal to the circle with diameter BC.

The inversion transforms the two lines to the two circles with diameters AB and AC respectively.

The family of equal circles, between the two lines is transformed to the chain of circles filling the arbelos.

Count the inscribed circles c

A theorem of Steiner (actually

d

[Steiner, Werke Bd I, pp. 47-51]

Switch to the [select-on-contour-tool] (CTRL+2). Catch and move point C.

Prove that the centers of circles c

Prove that c, e

See the file WooConstruction.html for some elegant ways to construct the first circle c

InvertingOnFamily.html

SteinerChain.html

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