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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 line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspective axis or homology ...

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 ...

257 is a Fermat prime, and the 257-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. An illustration of the 257-gon is not included ...

There are three theorems related to pedal circles that go under the collective title of the Fontené theorems. The first Fontené theorem lets DeltaABC be a triangle and P an ...

A great circle is a section of a sphere that contains a diameter of the sphere (Kern and Bland 1948, p. 87). Sections of the sphere that do not contain a diameter are called ...

An important theorem in plane geometry, also known as Hero's formula. Given the lengths of the sides a, b, and c and the semiperimeter s=1/2(a+b+c) (1) of a triangle, Heron's ...

The number M_2(n) = 1/nsum_(k=1)^(n^2)k (1) = 1/2n(n^2+1) (2) to which the n numbers in any horizontal, vertical, or main diagonal line must sum in a magic square. The first ...

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

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 ...