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Angle AOB is a central angle. A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). [1]
The inscribed angle theorem relates the measure of an inscribed angle to that of the central angle intercepting the same arc. The inscribed angle theorem appears as Proposition 20 in Book 3 of Euclid's Elements .
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.
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.
The degree of curvature is defined as the central angle to the ends of an agreed length of either an arc or a chord; [1] various lengths are commonly used in different areas of practice. This angle is also the change in forward direction as that portion of the curve is traveled.
The circular arc is said to subtend the angle, known as the central angle, at the centre of the circle. The angle subtended by a complete circle at its centre is a complete angle, which measures 2 π radians, 360 degrees, or one turn.
Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).
In circle O, angle AOB forms a central angle and defines a sector (shown in light red). Minor arc AB is formed by tracing the circle clockwise from A to B. Major arc BA is formed by tracing the circle clockwise from B to A. Date: 17 December 2011 13:51:44(UTC) (Originally uploaded at 2011-12-17 13:44:39) Source