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The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function alpha_(1151)=2cosA+sinA (1) corresponding ...

The Lucas tangents triangle (a term coined here for the first time) is the triangle DeltaT_AT_BT_C formed by the pairwise tangents of the Lucas circles of a given reference ...

The MacBeath circumconic is the dual conic to the MacBeath inconic, introduced in Dec. 2004 by P. Moses (Kimberling). It has circumconic parameters x:y:z=cosA:cosB:cosC, (1) ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

Ono (1914) conjectured that the inequality 27(b^2+c^2-a^2)^2(a^2+c^2-b^2)^2(a^2+b^2-c^2)^2<=(4K)^6 holds true for all triangles, where a, b, and c are the lengths of the ...

The orthographic projection is a projection from infinity that preserves neither area nor angle. It is given by x = cosphisin(lambda-lambda_0) (1) y = ...

The outer Napoleon circle, a term coined here for the first time, is the circumcircle of the outer Napoleon triangle. It has center at the triangle centroid G (and is thus ...

Let A^' be the outermost vertex of the regular pentagon erected outward on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...

A primitive right triangle is a right triangle having integer sides a, b, and c such that GCD(a,b,c)=1, where GCD(a,b,c) is the greatest common divisor. The set of values ...