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For fixed points A and B, the set of points M in the plane for which the angle ∠AMB is equal to α is an arc of a circle. The measure of ∠ AOB , where O is the center of the circle, is 2 α . The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2 θ that intercepts the same arc on the circle.
More generally, an angle subtended by an arc of a curve is the angle subtended by the corresponding chord of the arc. For example, a circular arc subtends the central angle formed by the two radii through the arc endpoints. If an angle is subtended by a straight or curved segment, the segment is said to subtend the angle.
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).
A triangle was formed of the base line, the subduction line, and a chord across the arc of the subtended angle. Currently the vertex opposite the base line does not extend as far as the chord. The east leg curves, shortening the west leg. The curvature demonstrates that the east leg is not as rigid as the west. [34]
When the arc reaches 60°, the chord length is exactly equal to the number of degrees in the arc, i.e. chord 60° = 60. For arcs of more than 60°, the chord is less than the arc, until an arc of 180° is reached, when the chord is only 120. The fractional parts of chord lengths were expressed in sexagesimal (base 60) numerals. For example ...
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 long-awaited $30 million runway expansion project at Middle Georgia Regional Airport, which Miller called a “game-changer,” will add 600 feet to lengthen the main runway to 7,100 feet ...
The solid angle of a sphere measured from any point in its interior is 4 π sr. The solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. The solid angle subtended at the corner of a cube (an octant) or spanned by a spherical octant is π /2 sr, one-eight of the solid angle of a sphere. [1]