Circle

In mathematics or geometry, a circle is a specific type of ellipse with zero eccentricity and two coinciding foci. A circle is often referred to as the locus of equidistant points drawn from the centre. The radius of a circle is the distance between its centre and its outside line. The diameter of a circle is defined as the line that splits it into two equal pieces and is also equal to twice the radius.

A circle is a fundamental two-dimensional form that is defined by its radius. The rings denote the plane’s inner and exterior areas. It is comparable to the line segment type. Consider the line segment curled around till its ends meet. Arrange the loop in such a way that it is perfectly round.

How to Draw a Circle

Here’s how you can draw a circle: 

• Take an empty piece of paper and make a single mark in the centre of it, naming it point O.
• Choose a random radius length, such as 3 cm.
• Maintain the reference zero mark on point O and randomly mark 3 cm away from it in all directions using a ruler.
• Make as many points as you like away from point O, but they must all be precisely 3 cm apart.
• After selecting a significant number of points, you may observe that the form begins to resemble a circle, which is just what a circle is.

Parts of a Circle

• The region bordered by two concentric circles is called an annulus. Essentially, it is a ring-shaped item.
• An arc is a circle’s linked curve.
• A sector is a rectangular rectangle defined by two radii and an arc.
• An area enclosed by a chord and an arc connecting its endpoints is called a segment. It’s worth noting that segments lack a central axis.
• The centre of a circle is its midway.
• A chord is a section of a line whose ends are on a circle.
• Diameter- A line segment that connects the circle’s two ends and is the circle’s greatest chord.
• A radius is a line segment that connects the circle’s centre to any point on the circle.
• A secant is a straight line that cuts a circle in half at two places. Additionally, it is referred to as an extended chord.
• A tangent is a coplanar straight line that intersects the circle at one point.

Radius is the piece of a circle’s circumference that connects the circle’s centre to any point on the circumference. The radius of a circle is indicated by the letters “R” or “r”.

Diameter is a line segment that contains both of the circle’s ends. It is twice the radius’s length, i.e. d = 2r. The radius of a circle is calculated using the diameter as the formula r= d/2.

Circumference of a Circle

A circle’s circumference is defined as the distance around it. ‘Perimeter’ is a technical term which is occasionally used as well, however this is not the case most of the time. It usually refers to the distance between polygons, which are forms composed of straight line segments.

The formula for the circumference of a circle is as follows:

C = 𝜋d = 2𝛱r

Where is 𝜋 = 22/7 or 3.14

Area of Circle Formula

The area of a circle is the volume of space that it occupies.

The formula for calculating the area of a circle is as follows: Area of a circle = 𝜋r2.

Properties of a Circle

Here are the properties of a circle you should know:

• A circle’s outside line is equidistant from its centre.
• The diameter of a circle divides it in half.
• Circles with identical radii are congruent.
• Circles of varying sizes or radii are comparable.
• The diameter of a circle is equal to the radius multiplied by two.

Solved Questions

• Find the circumference and area of a circle whose radius is 42cm. (Take 𝜋=22/7)

Answer: Circumference of the circle will be 2𝜋r = 2 x 22/7 x 42 = 264cm

Area of the circle will be 𝜋r2 = 22/7 x 42 x 42 = 5544cm

• Find the area of a circle whose circumference is 264cm.

Answer: Circumference of a circle is 2𝜋r which is equal to 264cm in this question.

2𝜋r = 264

2 x 22/7 x r = 264

r = 264 x 7 / 2 x 22

r = 42cm 

Area of the circle will be 𝜋r2 = 22/7 x 422 = 5544cm

Conclusion

To sum it all up:

• A circle is a closed two-dimensional curve with all points on its surface equidistant from the centre point. 
• The arc, chord, centre, diameter, radius, tangent, arc, sector and secant are the various components of a circle. 
• If “r” is the radius of the circle, the area and circumference of the circle are calculated as follows:
• A circle’s circumference is equal to 2𝜋r units.
• A circle’s area is equal to 𝜋r2 square units.