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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]
In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field.A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.
A central-force problem is said to be "integrable" if this integration can be solved in terms of known functions. If the force is a power law, i.e., if F ( r ) = a r n {\displaystyle F(r)=ar^{n}} , then u {\displaystyle u} can be expressed in terms of circular functions and/or elliptic functions if n {\displaystyle n} equals 1, -2, -3 (circular ...
This is an inscribed angle problem plus a question of orientation. The set of points P such that , = + is an arc of circle EA that joins E and A, of which the two radius leading to E and A form a central angle of 2(180° – 135°) = 2 × 45° = 90°.
Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere.
Since no triangle can have two obtuse angles, γ is an acute angle and the solution γ = arcsin D is unique. If b < c, the angle γ may be acute: γ = arcsin D or obtuse: γ ′ = 180° − γ. The figure on right shows the point C, the side b and the angle γ as the first solution, and the point C ′, side b ′ and the angle γ ′ as the ...
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.
Let θ 1 be the angle spanned by one side of the cyclic polygon as viewed from the center of the circumscribing circle. Similarly define the central angles θ 2, ..., θ n for the remaining n − 1 sides. Every Heronian triangle and every Brahmagupta quadrilateral has a rational value for the tangent of the quarter angle, tan θ k /4, for every ...