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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.
All positions on the eye-level line except the point of tangency are outside of the circle, and therefore the angle subtended by the painting from those points is smaller. 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.
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
The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
The James River Gorge is a water gap created by the James River in Central Virginia. The Gorge is 2,433 feet (742 m) [ 1 ] deep as measured from Highcock Knob 3,073 feet (937 m) [ 1 ] to the James River 640 feet (200 m) [ 1 ] and is approximately 9.3 miles (15.0 km) [ 2 ] long.
The Kootenay River [7] or Kootenai River [2] is a major river of the Northwest Plateau in southeastern British Columbia, Canada, and northern Montana and Idaho in the United States. It is one of the uppermost major tributaries of the Columbia River , the largest North American river that empties into the Pacific Ocean.