Three Constructions of Archimedean Circles in an Arbelos
نویسنده
چکیده
We give ruler and compass constructions of three Archimedean circles in an arbelos, each with the endpoints of a diameter on the smaller semicircles. In the first case, the diameter contains the intersection of the defining smaller semicircles of the arbelos. In the second case, these endpoints are the intersections of the smaller semicircles with the lines joining the endpoints of the base of the arbelos to a fixed point on the dividing perpendicular line. In the third case, the diameter containing these endpoints is parallel to the base line of the arbelos.
منابع مشابه
Ubiquitous Archimedean Circles of the Collinear Arbelos
For a point O on the segment AB in the plane, the area surrounded by the three semicircles with diameters AO, BO and AB erected on the same side is called an arbelos. It has lots of unexpected but interesting properties (for an extensive reference see [1]). The radical axis of the inner semicircles divides the arbelos into two curvilinear triangles with congruent incircles called the twin circl...
متن کاملThe Arbelos and Nine-Point Circles
We construct some new Archimedean circles in an arbelos in connection with the nine-point circles of some appropriate triangles. We also construct two new pairs of Archimedes circles analogous to those of Frank Power, and one pair of Archimedean circles related to the tangents of the arbelos.
متن کاملThe Arbelos with Overhang
We consider a generalized arbelos consisting of three semicircles with collinear centers, in which only two of the three semicircles touch. Many Archimedean circles of the ordinary arbelos are generalized to our generalized arbelos.
متن کاملThe Twin Circles of Archimedes in a Skewed Arbelos
Any area surrounded by three mutually touching circles is called a skewed arbelos. The twin circles of Archimedes in the ordinary arbelos can be generalized to the skewed arbelos. The existence of several pairs of twin circles, under certain conditions, is demonstrated.
متن کاملLamoenian Circles of the Collinear Arbelos
For a point T and a circle δ, if two congruent circles of radius r touching at T also touch δ at points different from T , we say T generates circles of radius r with δ, and the two circles are said to be generated by T with δ. If the generated circles are Archimedean, we say T generates Archimedean circles with δ. Frank Power seems to be the earliest discoverer of this kind Archimedean circles...
متن کامل