Circle and its Different Parts Class 9- Definition, Formulas, Properties & FAQs.

In math, a circle is a fundamental geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. This equidistant distance is known as the radius of a circle. Alternatively, a circle can be defined as the locus of points that are a fixed distance (the radius) away from a given point (the center).

Circles are characterized by their unique properties, such as having a constant circumference, which is the distance around the circle, and a constant area, which is the region enclosed by the circle. The diameter of a circle is the longest chord that passes through the center, and it is twice the length of the radius. Circles play a significant role in various fields, including mathematics, physics, engineering, and everyday life, due to their symmetrical and uniform properties, making them essential for calculations, constructions, and designs.

Definition of a Circle :

A circle is a round-shaped figure that has no corners or edges and it is equidistant from a fixed point.

Here are a few examples of Circles in everyday life :

1. Coins : Most coins, such as quarters, pennies, and dimes, are circular in shape.
2. Wheels : The wheels of vehicles like cars, bicycles, and trucks are circular.
3. Clocks and Watches : The face of analog clocks and watches is typically circular.

All Parts of a circle:

Circumference of a circle: The circumference is the arc length of the circle or the measurement of the boundary of the circle.

Center of a circle: The center of a circle is the midpoint where all radii intersect.

Chord of a circle: Chord of a Circle is a line segment inside the circle whose endpoints both lie on a circular arc.

Diameter of a circle: Longest chord of a circle is called the diameter of a circle. Diameter(D)=2r, where r is the radius of a circle.

Radius of a circle: Radius of a circle is the distance from the center of the circle to any point of it’s circumference. Radius(r) =D/2, where D is the diameter of a circle.

Tangent to a circle: A line that touches the circle at a single point is known as a tangent to a circle.

Secant of a circle: A straight line that intersects a circle in two points is called a secant of a circle.

Arc of a circle: The arc of a circle is defined as the part or segment of the circumference of a circle.

There are two types of arc : 1)minor arc and 2)major arc;

1. Minor arc is the shorter part of the circumference.
2. Major arc is the longer part of the circumference.

Segment of a circle: The region which is created by a secant or a chord with the corresponding arc of the circle is called the segment of a circle. The segment having a larger area is known as the major segment and the segment having a smaller area is known as the minor segment.

Annulus: The region bounded by two concentric circles. The shape of the annulus is like a ring.

Semicircle and Quadrant:

Semicircle: A semicircle is defined as a half circle formed by cutting the circle into two halves.

Quadrant: One-fourth section of a circle is called quadrant of a circle.

Formulas of Circle

Some important formulas related to circles include:

1. Circumference: C=2πr, where r is the radius of the circle.
2. Area: A =πr², where r is the radius of the circle.
3. Diameter: D = 2r, where D is the diameter and r is the radius of the circle.
4. Arc length: L= n/360×2πr, where n is the central angle(in degrees) subtended by the arc.
5. Sector area: A= n/360×πr² , where n is the central angle and r is the radius of the circle.
6. Chord length: l=2rsin(θ/2), where l is the length of the chord , r is the radius of the circle and θ is the central angle (in radians) subtended by the chord.
7. Area of semicircle =½×πr², where r is the radius of the circle.

Note – π=22/7 or 3.14

Properties of circles :

The important basic properties of circles are as follows:

1. The outer line of a circle is at equidistant from the centre.
2. The diameter of the circle divides it into two equals parts.
3. The diameter of the circle is the largest chord of the circle.

FAQs:

1. Name the largest chord of the circle?

Answer- Diameter.

2. What is circle for kids?

Answer- A circle is a round shaped figure.

3. Find the radius of the circle whose diameter is 10cm?

Answer- We know that,

r=D/2

=10/2

=5cm.

4. Find the diameter of the circle whose radius is 4cm?

Answer- We know that,

D=2r

=2×4

=8cm.

5. What is the value of pi(π)?

Answer- 22/7 or 3.14