Circle: Definition, Elements, Formulas and Example Problems

What comes to your mind when you hear about circles? You must be familiar with this flat shape.

A two-dimensional shape that has an area and a perimeter is called a plane shape. Paper with various shapes is known as a flat shape because it has a shape, but has no space.

Flat shapes consist of various shapes, namely circles, squares, triangles, rectangles, rhombuses, and so on. This article will focus on discussing the flat shape of a circle.

Definition of Circle

What is meant by a circle as a flat shape? Flat shapes that are composed of curves and not straight lines so that they do not include polygons are called circles. A special ellipse where the two foci coincide and the eccentricity is 0 can also be defined as a circle.

The circle is a flat figure that has no angles. You often encounter objects in the shape of a circle in everyday life, such as plates, car tires, cup holders, wall clocks, coins, and many more.

The characteristics of a circle are that it has a diameter that divides it into two balanced sides and has a total angle of 180 degrees. In addition, the constant diameter and radius connecting the center point to the circular arc point are also the characteristics of a circle.

A circle has one side with infinite circular fold symmetry as one of its properties. Then the nature of the circle also has an infinite circle rotational symmetry.

In various fields, the concept of a circle is widely applied. For example, the concept of the area of ​​a circle is often used to measure the area of ​​land or the area of ​​a circular object.

Then in various fields, the concept of circumference is also widely applied. For example, the concept of the circumference of a circle for solving problems regarding the radius or diameter of the wheel, the length of the track or the distance traveled, and other applications.

In mathematics, we often encounter circle elements in everyday life. It’s easy to recognize or distinguish a circle from other plane shapes. This flat shape is the only flat shape that has no corners.

In basic calculations, a circle as a two-dimensional shape only has area and circumference. In mathematics, You needs to know the elements of a circle first to find out the circumference to the total area.

The center point, radius, diameter, arc, chord, sector, and apothem are some of the elements in a circle that you need to know. The set of all points that are the same distance from a given point is called a circle.

It can be said that the set of dots is a way of formulating a circle in mathematics. In the formula above, the word “certain point” is called the center of the circle.

While the word “same distance” can be called the radius. In mathematics, the radius can be interpreted as a line segment connecting the center point to a point on a circle or as a measure of length.

Then the definition of a circle in general is one of the many types of two-dimensional plane shapes. A circle is formed from a collection of curved points that have the same length as the center of the circle itself.

A circle is a flat shape which is quite unique because it only has one curved side that meets each other without any angles. It can be said that a circle is a geometric shape and is flat. A curved curve covered with regular lines can be described as a circle shape.

Circle Elements

After understanding the meaning of a circle, now is the time for You to know the elements of a circle that can be applied to calculate the circumference and area of ​​a circle itself. Check out the following explanation.

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Illustration of Circle Elements (source: akupintar.id)

1. Center Point (P)

The center point is the first circle element that you need to know. The point directly in the center of the circle is called the center point.

The distance from the center point to all points on this one flat shape is always the same. The central point is often symbolized by using capital letters, such as A, O, P, Q, and so on.

2. Circle radius (r)

The next element is the radius of the circle. The radius can be interpreted as the distance between the center point of the circle and the point on the circle.

The radius of a circle is always the same because the distance between the center point and all points on the circle is the same. In mathematical formulas, the radius is often symbolized by the letter r or what is called the radius . Since they are the same length, this distance can stretch downwards, upwards, to the right, or to the left.

3.Diameter(d)

Diameter is the next circle element to be discussed. The length of the straight line that connects any two points on the circumference of a circle and passes through the center of the circle is the diameter.

It can be said that the value of the diameter of a circle is twice the value of the radius of the circle. Vice versa, the radius of a circle has a value of half the diameter. In mathematical formulas, diameter is often symbolized by the letter d.

4. Bow

The next circle element is the arc. What is meant by an arc as an element of a circle? The part of the circle in the form of a curved line is the definition of an arc.

There are two types of arcs in a circle, namely large arcs and small arcs. An arc that is longer than half the circumference of a circle is called a great arc.

While an arc whose length is less than half the circumference of a circle is called a minor arc. Curved lines, whether open or closed and intersecting with a circle, are called circular arcs.

5. Bowstring

The elements of the next circle are the bowstring. The straight line connecting any two points on a circle is called a chord.

The straight line connects any two points on the circumference of the circle, but does not pass through the center of the circle. If You has trouble imagining it, just imagine a circular bowstring just like the string on a crossbow.

6. Juring

The area flanked by two radii and a circular arc is the notion of the sector as a circle element. The wedge on the circle consists of two parts, namely the major sector and the minor sector.

Where the area in a circle bounded by the radius and arc of the circle is called the major sector. while the area in a circle bounded by the radius and the minor arc is referred to as the minor sector.

7. Part

The area flanked by a chord and a circular arc can be interpreted as a section. Then the division is divided into two, namely the large section and the small section.

The area bounded by the chord and the arc of the circle is called the great sector. Meanwhile, the area bounded by the chord and the small arc of the circle is called the minor section.

8. Apothem

The apothem becomes the element of the circle which will be discussed. The perpendicular line segment connecting the center point of the circle with the chord of the circle is defined as the apothem. Then the apothem can also be interpreted as the shortest distance of the chord with the center point of the circle.

9. Center Corner

The central angle is the next circle element to be discussed. An angle formed by the meeting of two chords with a point on the circumference of a circle is called the central angle.

10. Corner Circumference

The circumferential angle is the next element of the circle to be discussed. The angle formed by the intersection of two chords at a point on the circumference of a circle can be said to be the angle of circumference.

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Circle Formula

After recognizing the elements of a circle, now is the time for You to learn the formula for the circumference and area of ​​a circle. You needs to know the various circle formulas in order to get the right result. Here are some circle formulas that You must know as basic knowledge of mathematics.

1. Circumference Formula

The number that represents the length of the curve forming a circle is the meaning of the circumference of the circle. Just as the name suggests, the circumference is the longest arc in a circle. Just like the circumference of a circle, of course there is no arc that exceeds its length.

The longest arc on a circle is known as the circumference of the circle. It is not difficult to calculate the circumference of a circle.

There are two ways that You can use to calculate the circumference of a circle, namely if you know the diameter (d) or if you know the radius (r). You already knows that twice the radius of a circle is the diameter of a circle, right?

Here’s the formula for the circumference of a circle:

Illustration of the Circle Circumference Formula (source: akupintar.id)

You can use the following circle formula if what you are looking for is the radius of the circle and the circumference of the circle.

Illustration of the radius of a circle with the circumference of a circle (source: akupintar.id)

2. The formula for the area of ​​a circle

Actually, we have learned the circle formula when we were in elementary school. Because the formula for the area and the formula for the circumference of a circle look similar at first glance, the two formulas for a circle are often misleading.

You needs to study the formula for the area of ​​a circle more deeply so he doesn’t get fooled. After discussing the formula for the circumference of a circle, now is the time for You to learn the formula for the area of ​​a circle.

Come on, see the following review to understand it. You can calculate the area of ​​a circle by using the radius of the circle.

If in a known problem is the diameter, then you need to convert the diameter to the radius. How to? The trick is to divide the diameter by 2.

Problems example

Example of Circumference Questions

1. A circle has a radius of 10 cm, the circumference of the circle is …

2. There is a circular city park with a diameter of 10 meters. Determine the circumference of the circle!

3. A circle has a diameter of 14 cm. Determine the circumference of the circle!

4. Mr. Andi built a circular pond with a diameter of 7 meters. Mr. Andi intends to fence the pool with wooden planks. If Mr. Andi gives a distance between the logs of ½ meter, then how many wooden planks does Mr. Andi need to fence the pond he is building?

Example of a Circle Area Problem

1. A garden in the Bogor area has a diameter of 14 meters and will be planted with several types of flowers to decorate it. If every 11 m2 will be planted with one type of flower, then how many types of flowers will be planted in the garden?

2. If the area of ​​a circle has a circumference equal to 94.2 cm, that is…

3. The circumference of a circle is 32 cm, what is the area of ​​the circle?

4. A shop is in the shape of a circle with a diameter of 10 meters. Find the area of ​​the circular shop.

So, that’s an explanation of the circle formula, starting from the meaning, elements, to examples of problems . Has You understood the explanation above? Hopefully this article is useful and can add to your insight, You.