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Subtend
In geometry, an angle is subtended by an arc, line segment or any other section of a curve when its two rays pass through the endpoints of that arc, line segment or curve section. Conversely, the arc, line segment or curve section confined within the rays of an angle is regarded as the corresponding subtension of that angle. We also sometimes say that an arc is intercepted or enclosed by that angle. The precise meaning varies with context. For example, one may speak of the angle subtended by an arc of a circle when the angle's vertex is the centre of the circle. See also * Central angle * Inscribed angle External links Definition of subtended angle mathisfun.com, with interactive applet In computing, an applet is any small application that performs one specific task that runs within the scope of a dedicated widget engine or a larger program, often as a plug-in. The term is frequently used to refer to a Java applet, a program w ... How an object subtends an angle ''M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inscribed Angle
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint. The inscribed angle theorem relates the measure of an inscribed angle to that of the central angle subtending the same arc. The inscribed angle theorem appears as Proposition 20 on Book 3 of Euclid's ''Elements''. Theorem Statement The inscribed angle theorem states that an angle ''θ'' inscribed in a circle is half of the central angle 2''θ'' that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle. Proof Inscribed angles where 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'' an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
