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((,) is the center of a green circle.) Properties: a) Any two green circles intersect on the x-axis at the points / = (,), the poles of the orthogonal system of circles. That means, the x-axis is the radical line of the green circles.
Book 3 of Euclid's Elements deals with the properties of circles. Euclid's definition of a circle is: A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.
A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry, a circular segment or disk segment (symbol: ⌓) is a region of a disk [1] which is "cut off" from the rest of the disk by a straight line.
Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .
A circle (or line) is unchanged by inversion if and only if it is orthogonal to the reference circle at the points of intersection. [5] Additional properties include: If a circle q passes through two distinct points A and A' which are inverses with respect to a circle k, then the circles k and q are orthogonal.
The great circle g (green) lies in a plane through the sphere's center O (black). The perpendicular line a (purple) through the center is called the axis of g, and its two intersections with the sphere, P and P ' (red), are the poles of g. Any great circle s (blue) through the poles is secondary to g. A great circle divides the sphere in two ...
The Mall at Lexington Green is a hybrid enclosed shopping mall and outdoor lifestyle center in Lexington, Kentucky. Adjacent to Target and Fayette Mall, Lexington Green is located at the intersection of New Circle and Nicholasville Roads just north of the region's largest retail development. Lexington Green is positioned as an upscale retail ...
A satellite image of circular fields characteristic of center pivot irrigation, Kansas Farmland with circular pivot irrigation. Center-pivot irrigation (sometimes called central pivot irrigation), also called water-wheel and circle irrigation, is a method of crop irrigation in which equipment rotates around a pivot and crops are watered with sprinklers.