[alogo] Woo's Arbelos incircle construction

The arbelos on a segment AB is constructed by dividing it through a point C in two parts and drawing half-circles with diameters AC, CB and AB. Woo gave a very simple construction of the incircle D(DN) which is tangent to all three half-circles. J and K are the middles of the sides of the squares erected on AC, CB. The figure is self-explanatory.

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The reason for the validity of this construction is explained in Arbelos.html . The incircle D(DN) is the inverse of the circle with diameter GF with respect to a certain inversion with center at A. Symmetrically it is also the inverse of the circle with diameter IH with respect to a certain inversion with center at B. Hence the center D must lie on the intersection of AK and BJ.
This construction together with the three pictures below are discussed in:
Peter Y. Woo Simple Constructions of the Incircle of an Arbelos Forum Geometricorum Volume 1 (2001) pp. 133–136.

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[alogo] Three other constructions of the incircle of the arbelos


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See Also

Arbelos.html

References

Peter Y. Woo Simple Constructions of the Incircle of an Arbelos Forum Geometricorum Volume 1 (2001) pp. 133–136.

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