Question

Is a semicircle a segment of a circle? Can a semicircle be a sector of a circle? Give reasons for your answer.

Accepted Answer

A semicircle is a half-circle. It is formed by taking the complete circumference of a circle and dividing it into two equal parts.

A segment of a circle is a region bounded by a chord (a straight line connecting two points on the circle) and the arc (the curved part of the circle) intercepted by the chord. In the case of a semicircle, it is bounded by a diameter (which is a special type of chord) and the arc of the circle. The arc is exactly half of the entire circle's circumference. Therefore, a semicircle is a specific type of segment of a circle where the chord is a diameter, and it occupies exactly $180 °$ of the circle's central angle.

A sector of a circle is a region enclosed by two radii (lines drawn from the center of the circle to two points on the circle) and the arc between them. When considering a semicircle, it can also be viewed as a sector of a circle where the central angle is $180 °$ . So, a semicircle is a specific case of a sector where the central angle is $180 °$ .

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