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The nine-point circle, also called Euler's circle or the Feuerbach circle, is the circle that passes through the perpendicular feet H_A, H_B, and H_C dropped from the ...

The second Napoleon point N^', also called the inner Napoleon point, is the concurrence of lines drawn between polygon vertices of a given triangle DeltaABC and the opposite ...

The second Brocard point is the interior point Omega^' (also denoted tau_2 or Z_2) of a triangle DeltaABC with points labeled in counterclockwise order for which the angles ...

The low-level language of topology, which is not really considered a separate "branch" of topology. Point-set topology, also called set-theoretic topology or general ...

In 1989, P. Yff proved there is a unique configuration of isoscelizers for a given triangle such that all three have the same length and are concurrent (C. Kimberling, pers. ...

Let L, M, and N be lines through A, B, C, respectively, parallel to the Euler line. Let L^' be the reflection of L in sideline BC, let M^' be the reflection of M in sideline ...

The r-Hofstadter triangle of a given triangle DeltaABC is perspective to DeltaABC, and the perspector is called the Hofstadter point. The triangle center function is ...

The two-point form of a line in the Cartesian plane passing through the points (x_1,y_1) and (x_2,y_2) is given by y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1), or equivalently, ...

The second Fermat point X^' or F_2 (also known as the second isogonic center) can be constructed by drawing equilateral triangles on the inside of a given triangle and ...

Through a point K in the plane of a triangle DeltaABC, draw parallelians through a point as illustrated above. Then there exist four points K for which ...