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:

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

and so on.