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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. The angle θ is taken in the positive sense and must lie in the interval 0 < θ ≤ π (radian measure).
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint. The inscribed angle ...
The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (tangent chord angle). If the angle subtended by the chord at the centre is 90°, then ℓ = r √2, where ℓ is the length of the chord, and r is the radius of the circle.
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
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.
The chord of an angle subtends the arc of the angle. Ancient Greek and Hellenistic mathematicians made use of the chord. Given a circle and an arc on the circle, the chord is the line that subtends the arc. A chord's perpendicular bisector passes through the center of the circle and bisects the angle.
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A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...