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The Tucker circles are a generalization of the cosine circle and first Lemoine circle which can be viewed as a family of circles obtained by parallel displacing sides of the ...

A Tucker hexagon is a hexagon inscribed in a reference triangle that has sides which are alternately parallel and antiparallel to the corresponding sides of the triangle. ...

The Tucker cubic is the triangle cubic with trilinear equation secAsecBsecCsum_(cyclic)aalpha(b^2beta^2+c^2gamma^2) =alphabetagammasum_(cyclic)asecA(b^2sec^2B+c^2sec^2C). It ...

The Kuhn-Tucker theorem is a theorem in nonlinear programming which states that if a regularity condition holds and f and the functions h_j are convex, then a solution ...

The Tucker-Brocard cubic is the triangle cubic with trilinear equation abcsum_(cyclic)aalpha(b^2beta^2+c^2gamma^2)=alphabetagammasum_(cyclic)a^2(b^4+c^4). It passes through ...

A system of circles obtained by multiplying each radius in a coaxal system by a constant. The Tucker circles are a coaxaloid system (Johnson 1929, p. 277).

A sequence of circles which closes (such as a Steiner chain or the circles inscribed in the arbelos) is called a chain.

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

Consider a reference triangle DeltaABC and externally inscribe a square on the side BC. Now join the new vertices S_(AB) and S_(AC) of this square with the vertex A, marking ...

Johnson's theorem states that if three equal circles mutually intersect one another in a single point, then the circle passing through their other three pairwise points of ...