the interior of a circle is called a cabret
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exterior and interior of a circle
The union of a circle and its interior refers to the combination of all points on the circle itself and all points inside the circle. This forms a set that includes both the boundary of the circle and its interior region. In mathematical terms, this union is represented as the circle itself along with all points within the circle, denoted as the closed disk.
the set of points whose distance from the center of the circle is less than that of the radius.
That's a "sector" of the circle. It looks like a slice of pie.
The area bounded by an arc of circle and two radii is known as a "circular sector"