Understanding Circle Segments | Definition, Categorization, and Length Calculation

Segment (Circle)

In geometry, a segment of a circle refers to a part of the circle formed by two points on the circle and the arc between them

In geometry, a segment of a circle refers to a part of the circle formed by two points on the circle and the arc between them. Essentially, it is a portion of the circle’s circumference. The two points that define the segment are called endpoints.

A segment can be further categorized as either a minor segment or a major segment. A minor segment is the smaller portion of the circle between the endpoints, while a major segment is the larger portion between the endpoints.

Segments are distinguished from sectors, which are also portions of a circle but include the area enclosed by the arc and its corresponding central angle.

To find the length of a segment, you can utilize the properties of circles. One method is to use the formula for the circumference of a circle, which is 2πr, where “r” is the radius of the circle. By finding the lengths of the arcs formed by the endpoints and subtracting them from the circumference, you can determine the length of the segment.

For example, let’s say we have a circle with a radius of 5 units. If the endpoints form an arc of 120 degrees, we can calculate the length of the arc using the formula: (120/360) × 2π × r = (1/3) × 2π × 5 = 10π/3 units. Then, considering the whole circumference of the circle is 2π × r = 2π × 5 = 10π units, we can find the length of the segment by subtracting the length of the arc from the circumference: 10π – 10π/3 = 20π/3 units.

In summary, a segment of a circle refers to a portion of the circle’s circumference formed by two endpoints. It can be classified as either minor or major, and its length can be determined by subtracting the length of the arc formed by the endpoints from the circumference of the circle.

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