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Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the P-anticomplementary conjugate of U is the point where h(a,b,c,p,q,r,u,v,w) ...

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

Draw the perpendicular line from the intersection of the two small semicircles in the arbelos. The two circles C_1 and C_2 tangent to this line, the large semicircle, and ...

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the cevapoint of P and U is the point (pv+qu)(pw+ru):(qw+rv)(qu+pv) :(ru+pw)(rv+qw).

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 ...

The Droussent cubic is the triangle cubic with trilinear equation sum_(cyclic)(b^4+c^4-a^4-b^2c^2)aalpha(b^2beta^2-c^2gamma^2)=0. It passes through Kimberling centers X_n for ...

The excentral triangle, also called the tritangent triangle, of a triangle DeltaABC is the triangle J=DeltaJ_AJ_BJ_C with vertices corresponding to the excenters of DeltaABC. ...

A triangle DeltaA^'B^'C^' is said to be inscribed in a triangle DeltaABC if A^' lies on BC, B^' lies on CA, and C^' lies on AB (Kimberling 1998, p. 184). Examples include the ...

The triangle DeltaA^'B^'C^' formed by the points of pairwise intersection of the three intangents. It is not in perspective with DeltaABC. It has trilinear vertex matrix ...

The isogonal transform of a geometric object is the object obtained by collectively taking the isogonal conjugates of all its points.