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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 ...

In the plane, the reflection property can be stated as three theorems (Ogilvy 1990, pp. 73-77): 1. The locus of the center of a variable circle, tangent to a fixed circle and ...

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 ...

The region lying between two concentric circles. The area of the annulus formed by two circles of radii a and b (with a>b) is A_(annulus)=pi(a^2-b^2). The annulus is ...

Given a ship with a known constant direction and speed v, what course should be taken by a chase ship in pursuit (traveling at speed V) in order to intercept the other ship ...

The line segment KO^_ joining the symmedian point K and circumcenter O of a given triangle. It is the diameter of the triangle's Brocard circle, and lies along the Brocard ...

The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is P_n=(n-1)!. The number is (n-1)! instead ...

If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. A complete quadrangle is therefore a ...

The roulette traced by a point P attached to a circle of radius b rolling around the outside of a fixed circle of radius a. These curves were studied by Dürer (1525), ...

The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles (Kimberling 1998, p. 158). (The fact that the ...