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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^' ...

A Lie group is a smooth manifold obeying the group properties and that satisfies the additional condition that the group operations are differentiable. This definition is ...

If a points A^', B^', and C^' are marked on each side of a triangle DeltaABC, one on each side (or on a side's extension), then the three Miquel circles (each through 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 ...

Let a convex polygon be inscribed in a circle and divided into triangles from diagonals from one polygon vertex. The sum of the radii of the circles inscribed in these ...

Let two spheres of radii R and r be located along the x-axis centered at (0,0,0) and (d,0,0), respectively. Not surprisingly, the analysis is very similar to the case of the ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

The regular hexagon is the regular polygon with six sides, as illustrated above. The inradius r, circumradius R, sagitta s, and area A of a regular hexagon can be computed ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

The term "cylinder" has a number of related meanings. In its most general usage, the word "cylinder" refers to a solid bounded by a closed generalized cylinder (a.k.a. ...