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The tangential triangle is the triangle DeltaT_AT_BT_C formed by the lines tangent to the circumcircle of a given triangle DeltaABC at its vertices. It is therefore antipedal ...

There are two types of squares inscribing reference triangle DeltaABC in the sense that all vertices lie on the sidelines of ABC. The first type has two adjacent vertices of ...

Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...

The Simson line is the line containing the feet P_1, P_2, and P_3 of the perpendiculars from an arbitrary point P on the circumcircle of a triangle to the sides or their ...

Given a triangle DeltaABC, construct the contact triangle DeltaT_AT_BT_C. Now extend lines parallel to the sides of the contact triangle from the Gergonne point. These ...

Let P be a point with trilinear coordinates alpha:beta:gamma=f(a,b,c):f(b,c,a):f(c,ab) and P^' be a point with trilinear coordinates ...

Bipolar coordinates are a two-dimensional system of coordinates. There are two commonly defined types of bipolar coordinates, the first of which is defined by x = ...

If two projective pencils of curves of orders n and n^' have no common curve, the locus of the intersections of corresponding curves of the two is a curve of order n+n^' ...

The circumnormal triangle is an equilateral triangle with vertices on the circumcircle of a reference triangle DeltaABC obtained by rotating the circumtangential triangle by ...

The circumtangential triangle is an equilateral triangle formed by the three points X on the circumcircle of a reference triangle DeltaABC at which the line XX^(-1), where ...