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A triangle DeltaA^'B^'C^' is said to be circumscribed in a triangle DeltaABC if A lies on B^'C^', B lies on C^'A^', and C lies on A^'B^' (Kimberling 1998, p. 185). Examples ...

A coaxal system is a system of coaxal circles. A spectacular example is the set of circles (circumcircle, nine-point circle, orthocentroidal circle, orthoptic circle of the ...

For a unit speed curve on a surface, the length of the surface-tangential component of acceleration is the geodesic curvature kappa_g. Curves with kappa_g=0 are called ...

Let x be a point in an n-dimensional compact manifold M, and attach at x a copy of R^n tangential to M. The resulting structure is called the tangent space of M at x and is ...

The Yiu triangle DeltaO_AO_BO_C is the triangle formed by the centers of the Yiu circles. It has area where f(a,b,c) is a 12th-order polynomial and Delta is the area of the ...

An isoscelizer of an (interior) angle A in a triangle DeltaABC is a line through points I_(AB)I_(AC) where I_(AB) lies on AB and I_(AC) on AC such that DeltaAI_(AB)I_(AC) is ...

The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It ...

Let the inner and outer Soddy triangles of a reference triangle DeltaABC be denoted DeltaPQR and DeltaP^'Q^'R^', respectively. Similarly, let the tangential triangles of ...

The initial side of an angle theta drawn in angle standard position is the side lying on the positive x-axis. In general, viewing an angle as the amount of rotation about 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 ...