The region between a longest chord and an arc of a circle is called a semicircle because the longest chord is diameter and the region between a diameter and an arc is called semi circle

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A segment is the region between a chord and either of the arcs of the circle. It is important to understand the different parts of a circle to properly answer this question.

1. Circle: A circle is a closed curve in which all points are equidistant from a fixed point called the center.

2. Chord: A chord is a line segment that connects any two points on the circumference of the circle. It does not necessarily pass through the center.

3. Arc: An arc is a part of the circumference of a circle. It is the curved path between two points on the circumference.

Now, let's discuss the given options:

a) Sector: A sector is the region between two radii of a circle and the corresponding arc. It is like a slice of pie.

b) Semicircle: A semicircle is half of a circle. It is formed by cutting a circle along a diameter.

c) Segment: A segment is the region between a chord and either of the arcs of the circle. It is the area enclosed by the chord and the arc.

d) Quarter circle: A quarter circle is one-fourth of a circle. It is formed by cutting a circle into four equal parts along two perpendicular diameters.

Explanation:

To determine the correct answer, we need to understand the definition of a segment. A segment is the region between a chord and either of the arcs of the circle. It is the area enclosed by the chord and the arc. This means that a segment does not include the area inside the chord.

In contrast, a sector is the region between two radii of a circle and the corresponding arc. It includes the area inside the chord.

Similarly, a semicircle and a quarter circle refer to specific portions of a circle, but they do not describe the region between a chord and an arc.

Therefore, the correct answer is option 'C' - a segment.