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Let a_1, a_2, ..., a_n be scalars not all equal to 0. Then the set S consisting of all vectors X=[x_1; x_2; |; x_n] in R^n such that a_1x_1+a_2x_2+...+a_nx_n=c for c a ...

A 20-sided polygon. The regular icosagon is a constructible polygon, and the regular icosagon of unit side length has inradius r, circumradius R, and area A given by r = ...

The incentral circle is the circumcircle of the incentral triangle. It has radius R_I=(sqrt(abcf(a,b,c)f(b,c,a)f(c,a,b)))/(8Delta(a+b)(a+c)(b+c)), (1) where Delta is the area ...

Two rectangles, neither of which will fit inside the other, are said to be incomparable. This is equivalent to one rectangle being both longer and narrower. At least seven ...

Externally erect a square on the side BC. Now join the new vertices S_(AB) and S_AC of this square with the vertex A, marking the points of intersection Q_(A,BC) and ...

The inner Vecten circle is the circumcircle of the inner Vecten triangle. It has center at Kimberling center X_(642), which is the complement of the inner Vecten point ...

A triangle DeltaA^'B^'C^' is said to be inscribed in a triangle DeltaABC if A^' lies on BC, B^' lies on CA, and C^' lies on AB (Kimberling 1998, p. 184). Examples include the ...

The triangle DeltaA^'B^'C^' formed by the points of pairwise intersection of the three intangents. It is not in perspective with DeltaABC. It has trilinear vertex matrix ...

Three concurrent homologous lines pass respectively through three fixed points on the similitude circle which are known as the invariable points.

Two figures are said to be similar when all corresponding angles are equal, and are inversely similar when all corresponding angles are equal and described in the opposite ...