circle : introduction-concepts | complete revision class 10 maths
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Circle – Definition, Parts
What Is a Circle?
Interior and Exterior of a Circle
Parts of a Circle
A circle is a round-shaped figure that has no corners or edges.
In geometry, a circle can be defined as a closed shape, two-dimensional shape, curved shape.
Center of a Circle
The center of a circle is the center point in a circle from which all the distances to the points on the circle are equal. This distance is called the radius of the circle.
Here, point P is the center of the circle.
Interior and Exterior of a Circle
Consider the circle with center P and radius r. A circle has an interior and an exterior region.
Interior and Exterior of a Circle
All those points for which the distance is less than the radius of a circle lie in the interior of the circle. For example points P, Q, and R lie in the interior of the circle.
Semicircle:
Semi means half, so semicircle is half a circle. It is formed by cutting a whole circle along a line segment passing through the center of the circle. This line segment is called the diameter of the circle.
Quarter means one-fourth. So, a quarter circle is a quarter of a circle, formed by splitting a circle into 4 equal parts or a semicircle into 2 equal parts.
A quarter circle is also called a quadrant.
A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle.
Radius = C/2π
Radius of a Circle = d/2
Diameter of a Circle = 2r
A line segment passing through the center of a circle, and having its endpoints on the circle, is called the diameter of the circle.
Diameter = 2 × radius
Circumference:
The circumference of a circle is the distance around a circle. It is the same as the perimeter of other shapes.
Circumference of a Circle = 2πr
Chords of Circles:
A line segment with its endpoints lying on a circle is called the chord of the circle.
The diameter of a circle is its largest chord.
Arc of a Circle:
An arc is a part of the circle, with all its points on the circle. It is a curve that is a part of its circumference.
An arc that connects the endpoints of the diameter has a measure of 180° and it is called a semicircle.
An arc divides the circle into two parts. The smaller part is called the minor arc and the greater part is called the major arc.
A secant is a line that intersects a circle at exactly two points.
Tangent of a Circle:
A tangent is a line that intersects a circle at exactly one point.
Tangent of a Circle
Segments of a Circle:
A chord of a circle divides the circular region into two parts. Each part is called the segment of the circle.
The segment containing the minor arc is called the minor segment and the segment containing the major arc is called the major segment.
Segments of a Circle
The Sector of a Circle:
The sector of a circle is a part of the circle that is enclosed by two radii and an arc of the circle as a part of its boundary.
When two radii meet at the center of the circle to form the sector, it actually forms two sectors. A sector of a circle is called the minor sector if the minor arc of the circle is a part of its boundary. A sector is called the major sector if the major arc of the circle is a part of its boundary.
The area of a circle is the region enclosed inside the circle.
The area of a circle depends on the length of its radius.
Area = πr²
Circumference = 2πr
The distance around the circle is the circumference of the circle.
Circumference = 2πr
The value of π = 3.14 or 22/7