Twin circles

An arbelos is determined by three collinear points A, B, and C, and is the curvilinear triangular region between the three semicircles that have AB, BC, and AC as their diameters.

If the arbelos is partitioned into two smaller regions by a line segment through the middle point of A, B, and C, perpendicular to line ABC, then each of the two twin circles lies within one of these two regions, tangent to its two semicircular sides and to the splitting segment.

These circles first appeared in the Book of Lemmas, which showed (Proposition V) that the two circles are congruent.

[1] Thābit ibn Qurra, who translated this book into Arabic, attributed it to Greek mathematician Archimedes.

be the point where the larger semicircle intercepts the line perpendicular to the

The twin circles are the two circles inscribed in these parts, each tangent to one of the two smaller semicircles, to the segment

[3] Each of the two circles is uniquely determined by its three tangencies.

Constructing it is a special case of the Problem of Apollonius.

Alternative approaches to constructing two circles congruent to the twin circles have also been found.