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If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It ...

A lune is a plane figure bounded by two circular arcs of unequal radii, i.e., a crescent. (By contrast, a plane figure bounded by two circular arcs of equal radius is known ...

A perpendicular bisector CD of a line segment AB is a line segment perpendicular to AB and passing through the midpoint M of AB (left figure). The perpendicular bisector of a ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...

The radical lines of three circles are concurrent in a point known as the radical center (also called the power center). This theorem was originally demonstrated by Monge ...

A median A_1M_1 of a triangle DeltaA_1A_2A_3 is the Cevian from one of its vertices A_1 to the midpoint M_1 of the opposite side. The three medians of any triangle are ...

The van Aubel line is the line in the plane of a reference triangle that connects the orthocenter H and symmedian point K, and symmedian point of the orthic triangle. The ...

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...