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To construct a diameter parallel to a given line, choose the chord to be perpendicular to the line. The circle having a given line segment as its diameter can be constructed by straightedge and compass, by finding the midpoint of the segment and then drawing the circle centered at the midpoint through one of the ends of the line segment.
The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit.
A diameter is a line segment passing through the center of a circle or sphere with both its endpoints on the circle or sphere. It is the longest distance between two points of the circle or sphere; more generally the diameter of a set is the longest distance between two of its points.
The diameter symbol (Unicode character U+2300) is similar to the lowercase letter ø, and in some typefaces it even uses the same glyph, although in many others the glyphs are subtly distinguishable (normally, the diameter symbol uses an exact circle and the letter o is somewhat stylized).
Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.
This generalizes the diameter of a circle, the largest distance between two points on the circle. This usage of diameter also occurs in medical terminology concerning a lesion or in geology concerning a rock. A bounded set is a set whose diameter is finite. Within a bounded set, all distances are at most the diameter.
Circle with similar triangles: circumscribed side, inscribed side and complement, inscribed split side and complement. Let one side of an inscribed regular n-gon have length s n and touch the circle at points A and B. Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle on a diameter.
A page from Archimedes' Measurement of a Circle. Measurement of a Circle or Dimension of the Circle (Greek: Κύκλου μέτρησις, Kuklou metrēsis) [1] is a treatise that consists of three propositions, probably made by Archimedes, ca. 250 BCE. [2] [3] The treatise is only a fraction of what was a longer work. [4] [5]