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Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."

The first Morley cubic is the triangle cubic with trilinear equation sum_(cyclic)alpha(beta^2-gamma^2)[cos(1/3A)+2cos(1/3B)cos(1/3C)]. It passes through Kimberling centers ...

The first Neuberg circle is the circumcircle of the first Neuberg triangle. The center has center function (1) which is not a Kimberling center. Its radius is ...

A set in R^d formed by translating an affine subspace or by the intersection of a set of hyperplanes.

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 Garfield curve is the name sometimes given to the curve with polar equation r=thetacostheta when plotted from theta=-2pi to 2pi (Sisson and Szarvas 2016) because of its ...

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

The genesa is a mystical figure that correspond to a spherical cuboctahedron.

Two geometric figures are said to exhibit geometric congruence (or "be geometrically congruent") iff one can be transformed into the other by an isometry (Coxeter and ...