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The triangle transformation principle gives rules for transforming equations involving an incircle to equations about excircles.

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...

Let p be an irregular prime, and let P=rp+1 be a prime with P<p^2-p. Also let t be an integer such that t^3≢1 (mod P). For an irregular pair (p,2k), form the product ...

A polygon which has both a circumcircle (which touches each vertex) and an incircle (which is tangent to each side). All triangles are bicentric with R^2-x^2=2Rr, (1) where R ...

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

Let X be a normed space, M and N be algebraically complemented subspaces of X (i.e., M+N=X and M intersection N={0}), pi:X->X/M be the quotient map, phi:M×N->X be the natural ...

The contact triangle of a triangle DeltaABC, also called the intouch triangle, is the triangle DeltaC_AC_BC_C formed by the points of tangency of the incircle of DeltaABC ...

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

The first Brocard point Omega is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the ...

Let a convex cyclic polygon be triangulated in any manner, and draw the incircle to each triangle so constructed. Then the sum of the inradii is a constant independent of the ...