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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 ...
A side (regarded as a great circle arc) is measured by the angle that it subtends at the centre. On the unit sphere, this radian measure is numerically equal to the arc length. By convention, the sides of proper spherical triangles are less than π , so that 0 < a + b + c < 2 π {\displaystyle 0<a+b+c<2\pi } (Todhunter, [ 1 ] Art.22,32).
The arc length is then given by: = ... is the length of an arc of the circle, ... by inscribing a polygon of many sides in a circle, they were able to find ...
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]
Each point is associated with a unique great circle, called the polar circle of the point, which is the great circle on the plane through the centre of the sphere and perpendicular to the diameter of the sphere through the given point. As there are two arcs determined by a pair of points, which are not antipodal, on the great circle they ...
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.
Given a circle whose center is point O, choose three points V, C, D on the circle. Draw lines VC and VD: angle ∠DVC is an inscribed angle. Now draw line OV and extend it past point O so that it intersects the circle at point E. Angle ∠DVC intercepts arc DC on the circle. Suppose this arc includes point E within it.
An area formula for spherical triangles analogous to the formula for planar triangles. Given a fixed base , an arc of a great circle on a sphere, and two apex points and on the same side of great circle , Lexell's theorem holds that the surface area of the spherical triangle is equal to that of if and only if lies on the small-circle arc , where and are the points antipodal to and , respectively.