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If the square is instead erected internally, their centers form a triangle DeltaI_AI_BI_C that has (exact) trilinear vertex matrix given by (1) (E. Weisstein, Apr. 25, 2004). ...

Points, also called polar reciprocals, which are transformed into each other through inversion about a given inversion circle C (or inversion sphere). The points P and P^' ...

The first and second isodynamic points of a triangle DeltaABC can be constructed by drawing the triangle's angle bisectors and exterior angle bisectors. Each pair of ...

The Lucas central triangle (a term coined here for the first time) is the triangle DeltaL_AL_BL_C formed by the centers of the Lucas circles of a given reference triangle ...

The minimal enclosing circle problem, sometimes also known as the bomb problem, is the problem of finding the circle of smallest radius that contains a given set of points in ...

If perpendiculars A^', B^', and C^' are dropped on any line L from the vertices of a triangle DeltaABC, then the perpendiculars to the opposite sides from their perpendicular ...

The outer Napoleon triangle is the triangle DeltaN_C^'N_B^'N_A^' formed by the centers of externally erected equilateral triangles DeltaABE_C^', DeltaACE_B^', and ...

By analogy with the outer Napoleon triangle, consider the external erection of three squares on the sides of a triangle DeltaABC. These centers form a triangle DeltaO_AO_BO_C ...

The triangle bounded by the polars of the vertices of a triangle DeltaABC with respect to a conic is called its polar triangle. The following table summarizes polar triangles ...

If P be a point in the plane of an equilateral triangle DeltaABC, then the lengths of line segments AP, BP, and CP correspond the sides of a triangle, which is degenerate ...