Feuerbach's Theorem states that this entity is tangent to four other similar figures, with three of those being excircles.
The Jerabek antipode lies on this entity, as does the Kiepert antipode; both of the aforementioned antipodes also lend names to centers of namesake rectangular hyperbolae which also pass through special parts of this figure. The conical version of this entity deals with the midpoints and intersection points of the diagonals of a complete quadrangle. In a quadrilateral, these entities form a set named after Johnson. The trilinear coordinates for a characteristic of this entity are given as a triple ratio of the cosine of the pairwise differences of the angles. Feuerbach's Theorem states that this entity is tangent to four other similar figures, with three of those being excircles. The center of this figure is the midpoint of the orthocenter and the circumcenter of a triangle. For ten points, name this entity which passes through the midpoints of the segments formed by the orthocenter and the vertices, the feet of the altitudes and the midpoints of the sides, a famous circle in geometry.
The Jerabek antipode lies on this entity, as does the Kiepert antipode; both of the aforementioned antipodes also lend names to centers of namesake rectangular hyperbolae which also pass through special parts of this figure.
{nine}-{point} circle