Want to study the concept of circles? Register in the math program of Cuemath and get access to its online live lectures. With the help of the Cuemath learning program, you will be able to improve your calculation skills and your reasoning will also become strong. Read the below-given article to understand basics of a circle such as its definition, its parts, circumference of circle.
Defining circle in mathematics
In mathematics or geometry, a circle is a two-dimensional figure on which every point is equidistant from a specific point known as the center of the circle. Every line passing through the circle forms the line of reflection symmetry. A circle divides a plane into two parts, one is the interior region and the other is the exterior region.
What are the different parts of a circle?
Based on the positions and properties of the circle there are the following different parts of the circle:
- Annulus: Annulus is the region that is bounded by two concentric circles.
- Centre: Centre is the midpoint of a circle.
- Radius: Radius is the line segment that connects the center of a circle to any point on the boundary of the circle.
- Diameter: A diameter is the straight line segment that passes through the center of the circle and connects any two points on the boundary of the circle.
- Arch: Arch is referred to as the connected curve of a circle.
- Chord: A chord is a line segment that touches any two points on the boundary of a circle.
- Circumference: Circumference, also known as the perimeter is referred to as distance around the circle’s boundary.
- Sector: The sector of a circle is the region that is bounded by two radii and one arc.
- Segment: The segment of a circle is the region enclosed by a chord and the corresponding arc. One can see two types of segments in a circle, one is a minor segment and another one is a major segment.
- Secant: A straight line intersecting two points of the circumference of a circle is called a secant or extended chord.
- Tangent: A coplanar straight line that touches any one point of the boundary of a circle.
What are the formulas of a circle?
- Area of the circle: The area of a circle is referred to the amount of space occupied by the circle. Its area depends on the length of its radius. The mathematical formula to calculate the area of a circle is:
- Circumference or perimeter of a circle: The circumference or perimeter of a circle is the whole length of the boundary of the circle. The mathematical formula to calculate the circumference of a circle is:
Circumference = 2 × π × r
- Arc length of a circle: An arc of a circle is the part of a circle’s perimeter. The mathematical formula to calculate the arc length of a circle is:
Length of an arc: θ × r
- Area of the sector of a circle: An angle θ is made by the sector of a circle. Here, θ is measured in radians. The mathematical formula to calculate the area of a sector of a circle is:
Area of a sector of circle = (θ × r2) ÷ 2
- Length of Chord of a circle: To calculate the length of a chord, the angle made at the circle’s center by the chord and radius is to be known. The mathematical formula to calculate the length of the chord is:
Length of chord = 2 r sin(θ/2)
- Area of the segment of a circle: The mathematical formula to calculate the area of the segment of a circle is:
Area of segment = r2(θ − sinθ) ÷ 2
This article explains the concept of the circle in easy language. If facing difficulty to solve problems related to circle then go through the article and learn the circle formulas along with the area of circle formula and circle’s circumference formula.