Circles

A circle is a 2-D geometric shape widely used across our lives, from car wheels to coins and rings. We can easily find many examples of circles around us, such as clocks, plates, bangles, and even bubbles. In geometry, a circle is defined as a curved line that is always at the same distance from the center. Studying the properties of circle is important as it is applied in many fields such as engineering, architecture, geometry, astronomy and more. Circles may look simple, but they have some amazing properties and rules. In this article, we will define circles, their properties, theorems, formulas and their applications in real life.

 

Table of Contents

• What is a Circle?
• Properties of Circle
• Parts of a Circle
• Radius of a Circle
• Diameter of a Circle
• Circle Formulas
• Applications of Circle in Real-life:
• Circles Solved Examples
• Fun Circle Facts
• Conclusion
• FAQs on Circles

 

What is a Circle?

The word circle came from Greek word 'Kirkos' which means ring or hoop. A circle is a closed curved shape drawn by keeping equal distance from the center. Every point on the curve is at the same distance from the centre point. This fixed distance from center to any point on the curve is called the radius of a circle.

In simple words, a curve drawn around a fixed point without changing the distance is called a circle. The distance from the center to any point on the curve is called the radius of circle.

 

Properties of Circle

As each shape has a unique set of properties, circles also have their own properties that help to differentiate them from other curved shapes. Studying these properties and their applications is useful in maths as well as in real life. Some of the important properties of a circle are listed  below:

• The circumference or outline of a circle is equidistant from the center.

• A circle has no corners or edges.

• The diameter of a circle divides it into two halves called semicircle.

• Two circles are congruent to each other if they have the same radius.

• Radius of a circle is half its diameter.

• Equal chords are equidistant from the centre.

• A tangent to a circle is perpendicular to the radius at the point of contact.

• The angle in a semicircle is always a right angle (90°).

These properties help us easily solve many geometry problems related to circles.

 

Parts of a Circle

To understand circles better, let’s look at some important parts:

• Centre of a Circle: The point in the middle of circle that is equidistant from any point on its circumference is called the centre of a circle.

• Radius of a Circle: The distance from the centre to any point on the circle.

• Diameter of a Circle: A straight line passing through the centre, touching two points on the circle. It’s twice the radius.

• Circumference of Circle: The boundary or the outer line of the circle.

• Chord: A line that connects two points on the circle (not always through the centre).

• Arc: A part of the circumference.

• Sector: A "pizza slice" shaped part of the circle.

• Segment: The part between a chord and an arc.

• Segment - The part between a chord and an arc.

 

Radius of a Circle (r)

Radius of a circle is a line segment that starts from any point on the circle to the center of a circle. It is denoted by letter ‘r’ and plays a very important role in evaluating various properties like area and circumference of a circle. 

Diameter of a Circle (d) 

Diameter of a circle is defined as a line segment that starts from one point on a circle to another point while passing through the center of a circle. It is denoted by letter ‘d’ and is twice the radius of a circle. By knowing the diameter of a circle we can easily evaluate its radius and various properties like area and circumference.

 

Circle Formulas

The area and circumference of a circle is calculated using the formulas. By calculating the area and circumference of a circle you can easily estimate the quantity required for various tasks like filling water in a circular swimming pool.

 

The formulas to calculate the area of a circle:

• Area of a circle = π𝑟2, where r represents the radius of a circle.

The formulas to calculate the circumference of a circle:

• Circumference of a circle = 2 π𝑟

 

Applications of Circle in Real life

From cars to bicycles, wheels are perfect circles. They not only beautify things but they are functional too. For example, manhole covers are always round to prevent people from falling in. Additionally, we determine the dimensions of circular objects on daily basis to perform various tasks. Here are some of the major applications of circles in real-life:

• Architects build circular designs like domes and arch to beautify structures.

• Circular wheels support smooth movement and are used in variety of machines and transportation.

• Round shapes of foods like pizzas, cakes and cookies make it easier to share and serve.

• Circles help us understand waves, rotations, and motions in science.

• Storage containers are circular in shape optimizing storage space.

 

Circles Solved Examples

Here are some solved examples on circles that will help you to gain a clear understanding of circle concepts:

Example1: Find the area of a circular lid with radius as 20 cm.

Solution: We know that the radius of the circular lid is 20 cm

To find its area, use the formula:

Area =π𝑟2 

By inserting the value of π = 3.14 and r = 20 cm in formula, we get,

Area = 3.14×202

Area of circular disk = 1256cm2

 

Example 2: Diameter of a dinner plate is 10 cm. Calculate its area of the plate.

Solution:

Diameter of plate = 10 cm 

We know that the radius of a circle = d2 = 102 = 5 cm

To find its area, use the formula:

Area =π𝑟2 

By inserting the value of π = 3.14 and r = 5 cm in formula, we get,

Area = 3.14×52

Area of plate = 78.5cm2

 

Example 3: Determine its circumference of a swimming pool with diameter as 12 feet.

Solution: We know that, the formula to find the circumference of circular pool = 2πr 

By using the value of π & radius of pool, we can determine its circumference as:

2πr = 2 x 3.14 x 6

Circumference of a swimming pool = 37.68 ft

These examples show how common and useful circles are in everyday life.

 

Practice Problems

1. Find the area of a circle with radius 5 m.

2. Calculate the circumference of a circle with diameter = 8 cm.

3. What will be the diameter of a circle with circumference = 44 m?

4. Determine the radius of a circle if the area is 154 cm2

5. Find the amount of carpeting required for a circular room of radius 10 feet.

 

Fun Facts

• π (Pi) is the special number used to calculate the circumference and area of a circle.

• The area of a circle is calculated by the formula: A = πr²

• The circumference of a circle is found using: C = 2πr

 

Conclusion

While a circle might look like a basic object, it contains numerous amazing facts, beautiful theorems, and intriguing applications. Understanding properties of circles is important, not just in mathematics but in real life too. Applying this understanding of circles in geometry, along with all its properties and theorems, will make solving geometric questions effortless.

 

Frequently Asked Questions on Circles

Q1. What is called a circle?

Answer: A circle is a round shape no corners or straight sides. 

 

Q2. What are the 7 properties of a circle?

Answer: The 7 key properties include:

1. The circumference of a circle is equidistance from the center.

2. The diameter of a circle divides it into two halves called semicircle.

3. Two circles are congruent to each other if they have the same radius.

4. Radius of a circle is half its diameter.

5. Equal chords are equidistant from the centre.

6. A tangent to a circle is perpendicular to the radius at the point of contact.

7. The angle in a semicircle is always a right angle (90°).

These properties help us easily solve many geometry problems related to circles.

 

Q3. What is the formula for area of a circles?

Answer: Area enclosed within the boundary of a circle is called the area of a circle. Formula used to measure area of circle is πr2. Knowing how to calculate area of circle is helpful in solving geometric problems.

 

Q4. What are 5 examples of circles?

Answer: Clock, coin, plate, wheel, and bangle are common circular shapes in everyday life.

 

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