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Home > News & Articles > Segment of a Circle: Definitions, Types, Area with Formula, How to Calculate, Theorems, and Properties
Updated on 11th October, 2023 , 4 min read
A segment is the area of a circle between the chord and the arc. A circle is a route that a point equidistant from a single point on the plane may follow; this point is known as the circle's center, and the distance between it and that point is known as the circle's radius. A segment is a section of a circle's interior. A sector is the region that a segment encloses and the angle that a segment occupies. By deducting the triangle produced inside the sector from the sector that contains the segment, one may calculate the area of a circular segment.
A circle is a shape formed by all points on a plane that is at a particular distance from the center. The radius is the distance between any two points on a circle and the center. The circle has been known since before written history began. Natural circles, such as the full moon or a slice of round fruit, are frequent. The circle is the foundation for the wheel, which, together with related developments like gears, allows for the creation of much contemporary technology. The study of the circle has influenced the development of geometry, astronomy, and calculus in mathematics.
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A region enclosed by a chord and a matching arc located between the chord's ends is referred to as a segment of a circle. To put it another way, a circular segment is a section of a circle that divides from the remainder of the circle along a secant or chord. Segments are also the components that the arc of the circle divides into and connects to its ends through a chord. The center point is absent from the segments, it should be observed.
A segment of the circle is, by definition, the portion of a circle that is encompassed by a chord and its matching arc. The main segment and the minor segment are the two categories for segments of a circle. The major segment is the one with the bigger size, while the minor segment is the one with the lesser area.
Either radians or degrees can be used in the calculation to calculate segment area. The following are the formulae for a circle's segment-
Based on the segments of a circle, there are two fundamental theorems-
According to this theorem, the angle created at the point of contact between the tangent and the chord is equal to the angle created by the alternate segment on the circle's circumference via the chord's ends.
It asserts that angles created in the same circle segment are always equal.
A circle segment's characteristics are as follows-
In order to resolve issues concerning a circle segment-
A sector is made up of an arc and two circle radii. Together, these two radii plus the segment's chord make a triangle. As a result, the area of a circle's segment is calculated by deducting the triangle's area from the sector's area. i.e., the Area of a circle segment is equal to the sum of its sectors and triangles. Remember that the minor segment is in this place. A circle's minor portion is typically referred to as its segment.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. The area of a major segment of a circle is calculated by deducting its matching minor segment's area from the circle's overall area.
Ans. A circle's arc and chord together define a segment, which is the area within that region. There are two different sorts of segments: minor segments (created by minor arcs) and major segments (created by major arcs).
Ans. Yes, a semicircle is considered to be a segment. It is a circle's largest section. Additionally, a semicircle's diameter divides the circle into sectors and segments, dividing the circle's surface area.
Ans. A circle is a closed, two-dimensional object in which every point along its border is equally spaced from the central point. A semicircle may be a section of a circle. We are aware that a circle's diameter is also one of the circle's chords; in fact, it is the chord with the greatest length. Additionally, we are aware that the circumference of the semicircle is an arc of the circle. A semicircle is a section of the circle since it is enclosed by an arc and a chord.
Ans. Yes, the angles created by a given circle segment are equal. i.e., the angles formed by the same arc on the circle's circumference are equal.
Ans. According to the alternative segment theorem, the angle created at the point of contact between the tangent and the chord is equal to the angle created by the alternate segment on the circle's circumference via the chord's ends.
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