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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 river constantly evolves and as it does, meanders that were once a part of the river are abandoned in favor of a route that is more efficient for a river to take. As these old meanders are cutoff from the rest of the river, a new channel, or cutoff channel, is formed. Neck cutoff: a river bend intersects itself.
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.
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 thalweg of a river. In geography, hydrography, and fluvial geomorphology, a thalweg or talweg (/ ˈ t ɑː l v ɛ ɡ /) is the line or curve of lowest elevation within a valley or watercourse. [1] Its vertical position in maps is the nadir (greatest depth, sounding) in the stream profile.
The point of tangency can be constructed by the following steps: [4] [5] Reflect the bottom point of the painting across the line at eye-level. Construct the line segment between this reflected point and the top point of the painting. Draw the circle having this line segment as its diameter.
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, where the length of a chord subtended by a 112° arc is reported to be 99,29,5, it has a length of