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While some authors define "circumference" as distance around an arbitrary closed object (sometimes restricted to a closed curved object), in the work, the term "perimeter" is ...

Let ABCD be a quadrilateral with perpendicular polygon diagonals. The midpoints of the sides (a, b, c, and d) determine a parallelogram (the Varignon parallelogram) with ...

Given a set S of points in the plane, an enclosing circle is a circle for which all points S lie in its interior.

Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

The radical circle of the excircles has center at the Spieker center X_(10) and radius R_E=1/2sqrt((a^2b+ab^2+a^2c+abc+b^2c+ac^2+bc^2)/(a+b+c)). Its circle function is ...

If the tangents at B and C to the circumcircle of a triangle DeltaABC intersect in a point K_1, then the circle with center K_1 and which passes through B and C is called the ...

The first Neuberg circle is the circumcircle of the first Neuberg triangle. The center has center function (1) which is not a Kimberling center. Its radius is ...

The half-altitude circle is the circumcircle of the half-altitude triangle. The circle function is given by l=(f(a,b,c))/(128a^2b^3c^3cosAcosBcosC), (1) where (2) which is ...

Given three circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy (ace)/(bdf)=1 (Honsberger 1995).

The hexyl circle is the circumcircle of the hexyl triangle. Amazingly, its center is at the incenter I and its radius is 2R, where R is the circumradius. Its circle function ...