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2. 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 ...

3. 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.

4. List of trigonometric identities - Wikipedia

   en.wikipedia.org/wiki/List_of_trigonometric...

   The hypotenuse ¯ of the red-outlined triangle has length ⁡, so its side ¯ has length ⁡. The line segment A E ¯ {\displaystyle {\overline {AE}}} has length cos ⁡ 2 θ {\displaystyle \cos 2\theta } and sum of the lengths of A E ¯ {\displaystyle {\overline {AE}}} and D E ¯ {\displaystyle {\overline {DE}}} equals the length of A D ...

5. Circular segment - Wikipedia

   en.wikipedia.org/wiki/Circular_segment

   In the design of windows or doors with rounded tops, c and h may be the only known values and can be used to calculate R for the draftsman's compass setting. One can reconstruct the full dimensions of a complete circular object from fragments by measuring the arc length and the chord length of the fragment. To check hole positions on a circular ...

6. Sagitta (geometry) - Wikipedia

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

   In geometry, the sagitta (sometimes abbreviated as sag [1]) of a circular arc is the distance from the midpoint of the arc to the midpoint of its chord. [2] It is used extensively in architecture when calculating the arc necessary to span a certain height and distance and also in optics where it is used to find the depth of a spherical mirror ...

7. Ptolemy's table of chords - Wikipedia

   en.wikipedia.org/wiki/Ptolemy's_table_of_chords

   The fractional parts of chord lengths were expressed in sexagesimal (base 60) numerals. For example, where the length of a chord subtended by a 112° arc is reported to be 99,29,5, it has a length of + + = ¯, rounded to the nearest ⁠ 1 / 60 2 ⁠. [1] After the columns for the arc and the chord, a third column is labeled "sixtieths". For an ...