A circle is a two-dimensional shape where every point on the boundary is equidistant from a central point, called the center. The circle is actually the inner part of the circumference, i.e., the enclosed area inside the circle frame. This distance between the boundary and the center is called radius. The diameter is twice the radius, and it passes through the center, dividing the circle into two equal parts.
Below are some examples of circles with different circumferences. The colored part in each represents the circle:
More relevant components of the circle:
Radius: The distance from the center of the circle to any point on the circumference.
Diameter: A straight line passing through the center that connects two points on the circumference, equal to twice the radius.
The circle is the inner part, which is colored (green, blue, orange). The circumference is just the outline, here colored black.
Often, as you progress in your studies, you will have to calculate the area of the circle or the perimeter of the circumference (in the following articles we will see how this is done). The area of the circle is the region that is bounded by the circumference (by the contour). The perimeter of the circumference is the length of the contour of the circle.
When we talk about area we should say area of the circle and not area of the circumference, although it is true that sometimes it is used by mistake and, therefore, you may come across the expression "area of the circumference".
Example:
We have drawn a red dot for each of the illustrations. In the illustration on the right the dot is inside the area of the circle. We can also say that it is inside the perimeter of the circle.
In the middle illustration the dot is outside the area of the circle. We can also say that it is outside the perimeter of the circle. In the left illustration the red dot is on the perimeter of the circle.
Other key terms: center, radius, chord and diameter
Center
The center is the interior point equidistant to all points of the perimeter. Usually this point is marked with the letter O.
In these illustrations the center of the circle is marked with a black dot:
Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge
Question 1
If the radius of a circle is 5 cm, then the length of the diameter is 10 cm.
Incorrect
Correct Answer:
True
Question 2
Is there sufficient data to determine that
\( GH=AB \)
Incorrect
Correct Answer:
No
Question 3
Which figure shows the radius of a circle?
Incorrect
Correct Answer:
Radio
The radius is the distance between the center of the circle and any other point on the perimeter. It is denoted by the capital letter R or lowercase r as follows:
We will see that, intuitively, the larger the area of the circle and perimeter, the larger the length of the radius. Next we will learn more peculiarities of the relationship between them.
Chord
A chord is a straight line joining two points on the perimeter of the circle. We can draw an infinite number of chords on any circle. Note that the chord does not necessarily have to go through the center of the circle. For example, look at the chords in the illustration below:
Do you know what the answer is?
Question 1
Which diagram shows a circle with a point marked in the circle and not on the circle?
Incorrect
Correct Answer:
Question 2
M is the center of the circle.
Perhaps \( AB=CD \)
Incorrect
Correct Answer:
No
Question 3
The number Pi \( (\pi) \) represents the relationship between which parts of the circle?
Incorrect
Correct Answer:
Perimeter and diameter
Diameter
The diameter of the circle is the chord that passes exactly through the center. That is, it is the straight line joining two points of the perimeter passing through the center of the circle. It is usually denoted by the letter D. It looks like this:
If this article interests you, you may also be interested in the following articles:
If the radius of a circle is 5 cm, then the length of the diameter is 10 cm.
Incorrect
Correct Answer:
True
Question 2
Is there sufficient data to determine that
\( GH=AB \)
Incorrect
Correct Answer:
No
Question 3
Which figure shows the radius of a circle?
Incorrect
Correct Answer:
Exercise 8
Consigna
A construction company offered two tents for the kindergarten.
The circles are identical in each tent and form holes.
Which tent will generate more shade?
Solution
The shade depends on the area of the tent:
S1=7⋅8−4⋅π(22)2=
56−4π(22)2=43.44
S2=9⋅20−3⋅π(23)2=
9⋅20−3π(23)2=
9⋅20−6.75π=158.805
Answer
B
Review questions
What is a circle?
A circle is that part that is enclosed in a curved line called a circumference, in the following image the circle is the part that is blue.
Check your understanding
Question 1
Which diagram shows a circle with a point marked in the circle and not on the circle?
Incorrect
Correct Answer:
Question 2
M is the center of the circle.
Perhaps \( AB=CD \)
Incorrect
Correct Answer:
No
Question 3
The number Pi \( (\pi) \) represents the relationship between which parts of the circle?
Incorrect
Correct Answer:
Perimeter and diameter
What is the difference between circle and circumference?
The circle is the part that is inside the circumference, and the circumference is the line that surrounds the circle, let's see the difference with the following image.
What are the parts of a circle?
A circle is made up of a center, a radius, a diameter and a circumference.
Do you think you will be able to solve it?
Question 1
In which of the circles is the center of the circle marked?
Incorrect
Correct Answer:
Question 2
A point whose distance from the center of the circle is _______ than the radius, is outside the circle.
Incorrect
Correct Answer:
greater
Question 3
Where does a point need to be so that its distance from the center of the circle is the shortest?
Incorrect
Correct Answer:
Inside
What is a unit circle?
That which has a radius equal to 1 is called a unit circle.
What is the area of a circle and how is it calculated?
The Area of a circle is the surface, that is, the inner part of the whole circumference and we can calculate it with the formula A=πR2
Let's see an example:
Assignment:
Calculate the area of the following circle with D=9 cm
We know that the radius is half the diameter, therefore:
R=4.5 cm
π=3.14
Now we substitute this data into the area formula:
A=πR2=3.14(4.5 cm)2
3.14(20.25cm2)=63.585cm2
Answer
A=63.585cm2
Test your knowledge
Question 1
All ____ about the circle located in the distance ____ from the ____ circle
Incorrect
Correct Answer:
Point, equal, center
Question 2
Is it correct to say:
'the circumference of a circle'?
Incorrect
Correct Answer:
No
Question 3
Is it correct to say the area of the circumference?
Incorrect
Correct Answer:
Not true
Examples with solutions for Circle
Exercise #1
There are only 4 radii in a circle.
Step-by-Step Solution
A radius is a straight line that connects the center of the circle with a point on the circle itself.
Therefore, the answer is incorrect, as there are infinite radii.
Answer
False
Exercise #2
Which figure shows the radius of a circle?
Step-by-Step Solution
It is a straight line connecting the center of the circle to a point located on the circle itself.
Therefore, the diagram that fits the definition is c.
In diagram a, the line does not pass through the center, and in diagram b, it is a diameter.
Answer
Exercise #3
Which diagram shows a circle with a point marked in the circle and not on the circle?
Step-by-Step Solution
The interpretation of "in a circle" is inside the circle.
In diagrams (a) and (d) the point is on the circle, while in diagram (c) the point is outside of the circle.
Answer
Exercise #4
M is the center of the circle.
Perhaps AB=CD
Video Solution
Step-by-Step Solution
CD is a diameter, since it passes through the center of the circle, meaning it is the longest segment in the circle.
AB does not pass through the center of the circle and is not a diameter, therefore it is necessarily shorter.
Therefore:
AB=CD
Answer
No
Exercise #5
A point whose distance from the center of the circle is _______ than the radius, is outside the circle.
Step-by-Step Solution
Let's remember that the circle is actually the inner part of the circumference, meaning the enclosed area within the frame of the circumference.
Therefore, a point whose distance is greater than the center of the circle will necessarily be outside the circle.