|
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. The central angle is subtended by an arc between those two points, and the arc length is the central angle times the radius. The central angle is also known as the arc's angular distance. The size of a central angle Θ is 0°<Θ<360° оr 0<Θ<2π (radians). When defining or drawing a central angle, in addition to specifying the points A and B, one must specify whether the angle being defined is the convex angle (<180°) or the reflex angle (>180°). Equivalently, one must specify whether the movement from point A to point B is clockwise or counterclockwise. ==Formulas== *If the intersection points A and B of the legs of the angle with the circle form a diameter, then Θ=180° is a straight angle. (In radians, Θ=π.) Let ''L'' be the minor arc of the circle between points A and B, and let R be the radius of the circle.〔 interactive〕 *If the central angle Θ is subtended by ''L'', then Proof (for degrees): The circumference of a circle with radius R is 2πR, and the minor arc ''L'' is the (Θ/360°) proportional part of the whole circumference (see arc). So: : Proof (for radians): The circumference of a circle with radius R is 2πR, and the minor arc ''L'' is the (Θ/2π) proportional part of the whole circumference (see arc). So : *If the central angle Θ is not subtended by the minor arc ''L'', then the Θ is a reflex angle and *If a tangent at ''A'' and a tangent at ''B'' intersect at the exterior point ''P'', then denoting the center as ''O'', the angles ∠''BOA'' (convex) and ∠''BPA'' are supplementary (sum to 180°). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Central angle」の詳細全文を読む スポンサード リンク
|