The one-parameter family of triangles with common incircle and circumcircle is called a porisitic 1 system of triangles. The triangles of a poristic system can be rotated freely about the common incircle. However this motion is not a rigid body motion for the sidelengths of the triangle are changing. Surprisingly many triangle centers associated with the triangles of the poristic family trace circles while the triangle traverses the poristic family. Other points move on conic sections, some points trace more complicated curves. We shall describe the orbits of centers and some other points. Thereby we are able to answer open questions and verify some older results.

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Poristic Loci of Triangle Centers

In this article we study the set of triangles sharing a common incircle and a common centroid. It is shown that these triangles have their vertices on a conic easily constructible from the given data. It is also s hown that the cir- cumcircles of all these triangles are simultaneously tange nt to two fixed circles, hence their centers lie also on a conic.

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Rufus Crane

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Discussions: Another Poristic System of Triangles