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The lines containing the three points of the intersection of the three pairs of opposite sides of a (not necessarily regular) hexagon. There are 6! (i.e., 6 factorial) ...

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...

The area of the dodecagon (n=12) inscribed in a unit circle with R=1 is A=1/2nR^2sin((2pi)/n)=3.

Any symmetric polynomial (respectively, symmetric rational function) can be expressed as a polynomial (respectively, rational function) in the elementary symmetric ...

There are two different statements, each separately known as the greatest common divisor theorem. 1. Given positive integers m and n, it is possible to choose integers x and ...

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

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 ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

An inscribed angle in a semicircle is a right angle.

Assemble six 1×2×2 blocks and three 1×1×1 blocks into a 3×3×3 cube.