Definition:Circle/Arc

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.

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:

the arc $BC$ subtends the angle $\angle BAC$

the arc $BD$ subtends the angle $\angle BAD$

and so on.

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.

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.