# Definition:Circle/Arc

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## Definition

An **arc** of a circle is any part of its circumference.

### 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