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  2. Chord (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chord_(geometry)

    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.

  3. Circular segment - Wikipedia

    en.wikipedia.org/wiki/Circular_segment

    The arc length, from the familiar geometry of a circle, is = The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of ):

  4. Intersecting chords theorem - Wikipedia

    en.wikipedia.org/wiki/Intersecting_chords_theorem

    The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...

  5. Ptolemy's table of chords - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_table_of_chords

    When the arc reaches 60°, the chord length is exactly equal to the number of degrees in the arc, i.e. chord 60° = 60. For arcs of more than 60°, the chord is less than the arc, until an arc of 180° is reached, when the chord is only 120. The fractional parts of chord lengths were expressed in sexagesimal (base 60) numerals. For example ...

  6. Constant chord theorem - Wikipedia

    en.wikipedia.org/wiki/Constant_chord_theorem

    The lines and intersect the circle in and . The constant chord theorem then states that the length of the chord P 1 Q 1 {\displaystyle P_{1}Q_{1}} in k 2 {\displaystyle k_{2}} does not depend on the location of Z 1 {\displaystyle Z_{1}} on k 1 {\displaystyle k_{1}} , in other words the length is constant.

  7. Great-circle distance - Wikipedia

    en.wikipedia.org/wiki/Great-circle_distance

    The central angle between the two points can be determined from the chord length. The great circle distance is proportional to the central angle. The great circle chord length, , may be calculated as follows for the corresponding unit sphere, by means of Cartesian subtraction:

  8. Sagitta (geometry) - Wikipedia

    en.wikipedia.org/wiki/Sagitta_(geometry)

    In the following equations, denotes the sagitta (the depth or height of the arc), equals the radius of the circle, and the length of the chord spanning the base of the arc. As 1 2 l {\displaystyle {\tfrac {1}{2}}l} and r − s {\displaystyle r-s} are two sides of a right triangle with r {\displaystyle r} as the hypotenuse , the Pythagorean ...

  9. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    The sagitta (also known as the versine) is a line segment drawn perpendicular to a chord, between the midpoint of that chord and the arc of the circle. Given the length y of a chord and the length x of the sagitta, the Pythagorean theorem can be used to calculate the radius of the unique circle that will fit around the two lines: = +.