Circles – Explanation and Examples

The word circle comes from the Greek word krikos, which means ring. It is a circular arc equidistant from a fixed point called the center of a circle. The length of this arc is known as the circumference or perimeter of a circle. The utilization of circles is widely observed in several fields, ranging from the simplest to advanced mathematics, science, architecture, etc. Some of the real-world examples of circles are wheels, rings, pizzas, donuts, etc. The symmetric properties of circles are often used to design athletic tracks, buildings, watches, wheels, and so on.

Kids get introduced to circles during elementary or primary school. While proceeding to higher-grades, they study more complex concepts based on it. By middle school, kids start to learn geometry, and they also study all the properties of circles like the area of circle, the radius of a circle, circumference, diameter, and various word problems based on them. Kids must understand and acquire the knowledge of various concepts based on circles and their applications as it holds a great significance in our day-to-day life.

What is a circle?

A circle is one of the most basic geometric shapes formed by tracing a point on a plane equidistant from the other point called the center of the circle. This boundary is known as the circumference of the circle. The line joining the center of the circle to any point on its circumference is known as its radius. The area enclosed in the arc of the circle is called the area of a circle. It is calculated using the formula πr²

Examples: Let’s compare a large pizza area with a diameter of 16 inches with a small pizza with a diameter of 8 inches.

If the diameter of a large pizza is 16 inches, then its radius is 8 inches. 

Therefore the area of the large pizza will be π× 8² = 64π.

If the diameter of a small pizza is 8 inches, then its radius is 4 inches. 

Therefore the area of the small pizza will be π× 4² = 16π.

When you compare a large pizza area with a smaller pizza, you will see that the large pizza is four times larger than the smaller one.

Here are some useful terms associated with a circle:

Center of a Circle: 

The center of a circle is a point inside the circle that has the same distance from a point located anywhere on its boundary. It is usually represented by ‘O’.  

Radius: 

The radius of a circle is a line between the center and the circumference of the circle. It is denoted by r.

Circumference of Circle: 

The circumference of a circle is a boundary line with some distance from the Center of the circle. It is the length of a complete arc of a circle. It is calculated using the formula ‘2πr‘ where ‘r‘ denotes a circle radius.

Diameter: 

The circle’s diameter is a line that has endpoints on the circle boundary and passes through the center of the circle. The diameter D of a circle is twice the radius of a circle. i.e, D = 2r.

Arc: 

An arc is a segment of the circumference of a circle. If we place two points on a circle’s circumference, we will get a major arc and a minor arc.

Secant:

It is an extended chord, a coplanar straight line intersecting a circle in two points. 

Chord: 

A line segment joining any two points on the circumference of a circle is called a chord.

Tangent

It is a coplanar straight line that touches the circle at one point.

Conclusion:

The circle is an important math topic, and learning its properties and concepts is vital for kids to build lifelong knowledge. Understanding the basic concepts and underlying principles of a topic enables kids to grasp the core fundamentals quickly. Cuemath online classes encourage kids to learn math through reasoning, allowing them to gain an in-depth understanding of core concepts.

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