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A bicentric quadrilateral, also called a cyclic-inscriptable quadrilateral, is a four-sided bicentric polygon. The inradius r, circumradius R, and offset x are connected by ...

Given triangle DeltaA_1A_2A_3, let the point of intersection of A_2Omega and A_3Omega^' be B_1, where Omega and Omega^' are the Brocard points, and similarly define B_2 and ...

If S_1, S_2, and S_3 are three conics having the property that there is a point X, not on any of the conics, lying on a common chord of each pair of the three conics (with ...

A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing three equal squares such that each square ...

In 1803, Malfatti posed the problem of determining the three circular columns of marble of possibly different sizes which, when carved out of a right triangular prism, would ...

The midsphere, also called the intersphere, reciprocating sphere, or inversion sphere, is a sphere with respect to which the polyhedron vertices of a polyhedron are the ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...

An oval is a curve resembling a squashed circle but, unlike the ellipse, without a precise mathematical definition. The word oval derived from the Latin word "ovus" for egg. ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

A projection of the Veronese surface into three dimensions (which must contain singularities) is called a Steiner surface. A classification of Steiner surfaces allowing ...