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The Gallatly circle is the circle with center at the Brocard midpoint X_(39) and radius R_G = Rsinomega (1) = (abc)/(2sqrt(a^2b^2+a^2c^2+b^2c^2)), (2) where R is the ...

The hinge theorem says that if two triangles DeltaABC and DeltaA^'B^'C^' have congruent sides AB=A^'B^' and AC=A^'C^' and ∠A>∠A^', then BC>B^'C^'.

Given a geodesic triangle (a triangle formed by the arcs of three geodesics on a smooth surface), int_(ABC)Kda=A+B+C-pi. Given the Euler characteristic chi, intintKda=2pichi, ...

Three concurrent homologous lines pass respectively through three fixed points on the similitude circle which are known as the invariable points.

Given a point P in the interior of a triangle DeltaA_1A_2A_3, draw the cevians through P from each polygon vertex which meet the opposite sides at P_1, P_2, and P_3. Now, ...

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

The correspondence which relates the Hanoi graph to the isomorphic graph of the odd binomial coefficients in Pascal's triangle, where the adjacencies are determined by ...

Multisection of a mathematical quantity or figure is division of it into a number of (usually) equal parts. Division of a quantity into two equal parts is known as bisection, ...

The centroid of the four points constituting an orthocentric system is the center of the common nine-point circle (Johnson 1929, p. 249). This fact automatically guarantees ...

Given a pair of orthologic triangles, the point where the perpendiculars from the vertices of the first to the sides of the second concur and the point where the ...