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The second Morley adjunct triangle has trilinear vertex matrix [2 sec[1/3(C-2pi)] sec[1/3(B-2pi)]; sec[1/3(C-2pi)] 2 sec[1/3(A-2pi)]; sec[1/3(B-2pi)] sec[1/3(A-2pi)] 2]. The ...

The third Morley adjunct triangle has trilinear vertex matrix [2 sec[1/3(C-4pi)] sec[1/3(B-4pi)]; sec[1/3(C-4pi)] 2 sec[1/3(A-4pi)]; sec[1/3(B-4pi)] sec[1/3(A-4pi)] 2]. The ...

The Tixier point X_(476) is the reflection of the focus of the Kiepert parabola (X_(110)) in the Euler line. It has equivalent trilinear center functions X_(476) = ...

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_(179) called the first Ajima-Malfatti point ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

The Steiner deltoid is the envelope of the Simson lines of a triangle. Its circumcircle is the Steiner circle, and its incircle is the nine-point circle. The triangle formed ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center (i.e., the polygon is both equiangular ...