The triangle that is externally tangent to the excircles and forms their triangular hull is called the extangents triangle (Kimberling 1998, p. 162). It is homothetic to the orthic triangle, and the homothetic center is known as the Clawson point.
The extangents triangle has trilinear vertex matrix
(1)
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where , , , or equivalently,
(2)
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It has area
(3)
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where is the area of .
The circumcircle of the extangents triangle is the extangents circle.
Its incenter coincides with the circumcenter of triangle , where are the excenters of . The inradius of the incircle of is
(4)
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where is the circumradius of , is the inradius, and are the exradii (Johnson 1929, p. 192).