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Let one n-gon be inscribed in a circle, and let another n-gon be tangential to that circle at the vertices of the first n-gon. Then from any point P on the circle, the product of the perpendicular distances from P to the sides of the first n-gon equals the product of the perpendicular distances from P to the sides of the second n-gon. [13]
Circle Pines was founded as a planned cooperative community in which homeowners owned equal shares in the cooperative association which owned and developed the community. The name was selected because the cooperative movement in the United States in the 1940s used a circle encompassing two pine trees as its symbol.
In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3 ...
The sum of the squared distances from the vertices of a regular n-gon to any point on its circumcircle equals 2nR 2 where R is the circumradius. [4]: p. 73 The sum of the squared distances from the midpoints of the sides of a regular n-gon to any point on the circumcircle is 2nR 2 − 1 / 4 ns 2, where s is the side length and R is the ...
An apartment of a generalized n-gon is a cycle of length 2n. The root subgroup of a root is the subgroup of automorphisms of a graph that fix all vertices adjacent to one of the inner vertices of the root. A Moufang n-gon is a thick generalized n-gon (with n>2) such that the root subgroup of any root acts transitively on the apartments ...
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The edges of the two regular polygons are assumed to have the same length. A point z attached rigidly to the n-gon traces out an arch consisting of n circular arcs before repeating the pattern periodically. This curve is called a trochogon — an epitrochogon if the n-gon rolls outside the m-gon, and a hypotrochogon if it rolls inside the m-gon ...
Heavy machinery is seen Thursday at the site of a massive sinkhole that formed off Interstate 80 in New Jersey, just west of New York City, as crews evaluate the depression to design a repair.