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Archimedes' twin circles
In geometry, specifically in the study of the arbelos, the Archimedes' circles are two special circles associated with it.
Specifically, let , , and be the three corners of the arbelos, with between and . Let be the point where the larger semicircle intercepts the line perpendicular to the through the point . The segment divides the arbelos in two parts. The Archimedes' circles are the two circles inscribed in these parts, each tangent to one of the two smaller semicircles, to the segment , and to the largest semicircle.〔
These circles are named after the Greek mathematician Archimedes, who defined them and showed that they are congruent, whatever the sizes of the semicircles and . This is proposition 5 of his ''Book of Lemmas''.〔 The circles are also known as the Archimedean circles, Archimedean twins, or other similar names.〔
==Construction==
Each of the two circles is uniquely determined by its three tangencies. Constructing it is a special case of the Problem of Apollonius.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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