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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.
Case: One chord is a diameter. Let O be the center of a circle, as in the diagram at right. Choose two points on the circle, and call them V and A. Draw line OV and extended past O so that it intersects the circle at point B which is diametrically opposite the point V. Draw an angle whose vertex is point V and whose sides pass through points A ...
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).
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.
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 ...
Downcutting, also called erosional downcutting, downward erosion or vertical erosion, is a geological process by hydraulic action that deepens the channel of a stream or valley by removing material from the stream's bed or the valley's floor. The speed of downcutting depends on the stream's base level, the lowest point to which the stream can ...
Grand Canyon, Arizona, at the confluence of the Colorado River and Little Colorado River. A canyon (from Spanish: cañón; archaic British English spelling: cañon), [1] gorge or chasm, is a deep cleft between escarpments or cliffs resulting from weathering and the erosive activity of a river over geologic time scales. [2]
On the north coast is the River Camel and the River Taw. In Essex are the River Blackwater and River Crouch. Italy: The Fiordo di Furore on the Amalfi Coast in Campania is a ria, despite its name. Malta: Grand Harbour and Marsamxett Harbour; Croatia: Porto Quieto, Lim, Raša, Novsko Ždrilo, Karinsko Ždrilo, Zrmanja, Krka, Morinje, Ploče ...