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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 ...
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.
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 arc length, from the familiar geometry of a circle, is = The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of ):
The golden angle is the angle subtended by the smaller (red) arc when two arcs that make up a circle are in the golden ratio. In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as ...
Let 'arc AB' denote an arc whose two extremities are A and B of a circle with center 'O'. If a perpendicular BM is dropped from B to OA, then: jyā of arc AB = BM; koti-jyā of arc AB = OM; utkrama-jyā of arc AB = MA; If the radius of the circle is R and the length of arc AB is s, the angle subtended by arc AB at O measured in radians is θ ...
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.
In Euclidean geometry, an arc (symbol: ⌒) is a connected subset of a differentiable curve. Arcs of lines are called segments, rays, or lines, depending on how they are bounded. A common curved example is an arc of a circle, called a circular arc. In a sphere (or a spheroid), an arc of a great circle (or a great ellipse) is called a great arc.