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The anticomplement of a point P in a reference triangle DeltaABC is a point P^' satisfying the vector equation P^'G^->=2GP^->, (1) where G is the triangle centroid of ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

The Parry point is one of the two intersections of the Parry circle and the circumcircle of a triangle (the other is the focus of the Kiepert parabola, which is Kimberling ...

An elementary theorem in geometry whose name means "asses' bridge," perhaps in reference to the fact that fools would be unable to pass this point in their geometric studies. ...

Divide a triangle by its three medians into six smaller triangles. Surprisingly, the circumcenters O_(AB), O_(BA), etc. of the six circumcircles of these smaller triangles ...

The Neuberg A_1-circle is the locus of the polygon vertex A_1 of a triangle on a given base A_2A_3 and with a given Brocard angle omega. From the center N_1, the base A_2A_3 ...

The point on a line segment dividing it into two segments of equal length. The midpoint of a line segment is easy to locate by first constructing a lens using circular arcs, ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

Define the first Brocard point as the interior point Omega of a triangle for which the angles ∠OmegaAB, ∠OmegaBC, and ∠OmegaCA are equal to an angle omega. Similarly, define ...

The exterior angle bisectors (Johnson 1929, p. 149), also called the external angle bisectors (Kimberling 1998, pp. 18-19), of a triangle DeltaABC are the lines bisecting the ...