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The points of tangency of the Lucas inner circle with the Lucas circles are the inverses of the vertices A, B, and C in the Lucas circles radical circle. These form the Lucas ...

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 three circumcircles through the triangle centroid G of a given triangle DeltaA_1A_2A_3 and the pairs of the vertices of the second Brocard triangle are called the McCay ...

The Moses-Longuet-Higgins circle is the radical circle of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c-a, c+a-b, and ...

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

Oloa (2010, pers. comm., Jan. 20, 2010) has considered the following integrals containing nested radicals of 1/2 plus terms in theta^2 and ln^2costheta: R_n^- = (1) R_n^+ = ...

In the arbelos, consider the semicircles K_1 and K_2 with centers A and C passing through B. The Apollonius circle K_3 of K_1, K_2 and the large semicircle of the arbelos is ...

The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle DeltaS_AS_BS_C. Its center has center function ...

The Stevanovic circle is a central circle with center X_(650), which has center function alpha_(650)=cosB-cosC, (1) It has radius (2) It has circle function ...

The de Longchamps line is central line L_(32) with trilinear equation a^3alpha+b^3beta+c^3gamma=0 (Droussent 1953; Kimberling 1998, p. 150) which is the anticomplement of the ...