Definition:Circle/Arc
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Definition
An arc of a circle is a part of its circumference between two given points.
Hence for two given points $A$ and $B$ on the circumference of a circle, there are two such arcs so defined.
Angle Subtended by Arc
The angle subtended by an arc of a circle is the angle formed by the two radii from the center of the circle to the two endpoints of the arc.
In the above diagram:
and so on.
Major Arc
Let $a$ and $b$ be two points on the circumference of a circle.
The major arc joining $a$ and $b$ is the longer of the two arcs joining $a$ and $b$.
In the above diagram:
- the arc $ECBDF$ is the major arc defined by $E$ and $F$
- the arc $CEFDB$ is the major arc defined by $B$ and $C$
and so on.
Minor Arc
Let $a$ and $b$ be two points on the circumference of a circle.
The minor arc joining $a$ and $b$ is the shorter of the two arcs joining $a$ and $b$.
In the above diagram:
- the arc $EF$ is the minor arc defined by $E$ and $F$
- the arc $BC$ is the minor arc defined by $B$ and $C$
and so on.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): arc: 1 b.
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $5$: Eternal Triangles: The origins of trigonometry
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): arc (of a curve)
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): arc (of a curve)