Whats a chord geometry11/25/2023 ![]() Radius of Circle - (Measured in Meter) - Radius of Circle is the length of any line segment joining the center and any point on the Circle. One advantage of this choice of radius was that he could very accurately approximate the chord of a small angle as the angle itself. Chord Length of Circle - (Measured in Meter) - Chord Length of Circle is the length of a line segment connecting any two points on the circumference of a Circle. The number 1 ( b / d) 2 can be any value between 0 and 1, depending on b, so the length A C can be anything between 0 and d. A B + B C r 2 b 2 + r 2 b 2 2 r 2 b 2 d 1 ( b / d) 2. Toomer, Hipparchus used a circle of radius 3438' (=3438/60=57.3). The triangles A B O, C B O are right-angled at B. It was then a simple matter of scaling to determine the necessary chord for any circle. Ancient chord tables typically used a large value for the radius of the circle, and reported the chords for this circle. The half-angle identity greatly expedites the creation of chord tables. The chord function satisfies many identities analogous to well-known modern ones: Hipparchus is purported to have written a twelve volume work on chords, not extant, so presumably a great deal was known about them. Much as modern trigonometry is built on the sine function, ancient trigonometry was built on the chord function. The last step uses the half-angle formula. By taking one of the points to be zero, it can easily be related to the modern sine function: ![]() ![]() The chord of an angle is the length of the chord between two points on a unit circle separated by that angle. 00:00:29 5 Theorems and Definitions involving Chords of a Circle. The chord function is defined geometrically as in the picture to the left. The first known trigonometric table, compiled by Hipparchus, tabulated the value of the Chord function for every 7.5 degrees. Chords which are having the same length are at equidistant from the center of the circle and the chords which are at equidistant from the center are of equal length.Chords were used extensively in the early development of trigonometry.The line that bisects the chord from the center of the circle is perpendicular to the chord and that line is referred to as the perpendicular bisector of the chord.A chord of a circle is a line that joins the two points on the boundary of the circle and it is called a secant if the chord is extended external to the circle.A circle is a combination of points in a place that is at equidistant from the center O. ![]() OX=OY(Distance from the center are equal)īy SSS rule, ∆AOX≅∆COY and by RHS criterion, ∠ AOX = ∠ COY=90°, Regarding the details in the above theorem, Proof: AB and CD are two chords of a circle with center O, Both chords are at an equal distance from the center O, we have to prove that AB=CD Theorem 6: Two Chords of a circle which are at the same distance from the Center O are equal in length (Converse of Theorem 5) This proves that OX=OY, so two chords are at equal distance from the center O X bisects the AB as it is perpendicular to AB and as the same Y bisects the CD as it is perpendicular to CDīy SSS rule ∆AOX≅∆COY and by RHS criterion, ∠ AOX = ∠ COY=90°, The distance of AB from the center is marked as X and The distance of CD from the center is marked as Y Proof: AB and CD are two chords of a circle with center O and we have to prove that AB and CD are at equal distances from center O Theorem 5: Both the Equal chord of a circle are at equal distance from the center of a circle ![]()
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