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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 inverse of the central angle arc length series above may be found on page 8a of Rapp, Vol. 1, [2] who credits Ganshin. [3] An alternative to using the inverse series is using Newton's method of successive approximations to θ 12 {\displaystyle \theta _{12}} .
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.
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 ...
The inscribed angle theorem relates the measure of an inscribed angle to that of the central angle subtending 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.
The minor sector is shaded in green while the major sector is shaded white. A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the minor sector and the larger being the major sector. [1]
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.