The circle is actually the inner part of the circumference, i.e., the enclosed area inside the circle frame.

Below are some examples of circles with different circumferences. The colored part in each represents the circle:

The circle is actually the inner part of the circumference, i.e., the enclosed area inside the circle frame.

Below are some examples of circles with different circumferences. The colored part in each represents the circle:

The number Pi \( (\pi) \) represents the relationship between which parts of the circle?

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.

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:

Test your knowledge

Question 1

M is the center of the circle.

In the figure we observe 3 diameters?

Question 2

Is there sufficient data to determine that

\( GH=AB \)

Question 3

M is the center of the circle.

Perhaps \( MF=MC \)

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.

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

M is the center of the circle.

Perhaps \( AB=CD \)

Question 2

Which diagram shows a circle with a point marked in the circle and not on the circle?

Question 3

Which figure shows the radius of a circle?

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:**

- The circumference
- The center of the circumference
- Radius
- Diameter
- Pi
- Perimeter of the circle
- Circular area
- Arcs in a circle
- Chords in a circle
- Central angle in a circle
- Perpendicular to the chord from the center of the circle
- Inscribed angle in a circle

**In** **Tutorela**** you will find a variety of articles about mathematics**.

**Assignment:**

Given the circumference of the figure

The diameter of the circle is $13$,

**Solution**

It is known that the diameter of the circle is twice its radius, i.e. it is possible to know the radius of the circle in the figure.

$13:2=6.5$

To find the area of the circle, we replace the data we have in the formula for the calculation of the circle

$A=\pi\times R²$

**We replace the data we have:**

$A=\pi\times6.5²$

$A=\pi42.25$

**Answer**

$42.25\pi$

Check your understanding

Question 1

Is it correct to say the area of the circumference?

Question 2

All ____ about the circle located in the distance ____ from the ____ circle

Question 3

In which of the circles is the center of the circle marked?

**Request**

Given an equilateral triangle in a circle

What is the area of the circle?

**Solution**

Recall first the theorem that a circumferential angle that is inclined about the diameter is equal to $90^o$ degrees.

That is, the triangle inside the circle is a right triangle and isosceles, so we can use the Pythagorean formula.

We replace the data we have with the Pythagorean formula

$X=Diámetro$

$(\sqrt{2})²+(\sqrt{2})²=X²$

The root cancels the power and therefore we obtain that

$2+2=X²$

That is

$X²=4$

The root of $4$ is $2$ and therefore the diameter is equal to $2$ and the radius is equal to half of the diameter and therefore it is equal to $1$

Therefore we obtain that the diameter is equal to $2$

And the radius is $1$

Then we add the formula for the area of the circle

**Answer**

$π$

**Given the semicircle:**

**Consigna**

Calculate its area

**Solution**

Since we know that it is a semicircle we can conclude that the base of the semicircle is the diameter.

We know that the diameter is twice the radius and therefore we can know the radius of the circle.

$Diámetro = 14$

$14:2=7$

$Radio = 7$

The formula for calculating the area of the circumference is

$A=\pi\times R²$

We replace the data in the formula

$A=\pi\times 7²$

$A=\pi\times 49$

Since the formula was the area of the semicircle we divide the area of the circle by $2$ and get the answer.

$\pi49:2=24.5\pi$

**Answer**

$\pi49:2=24.5\pi$

Do you think you will be able to solve it?

Question 1

In which of the circles is the point marked in the circle and not on the circumference?

Question 2

Which diagram shows the radius of a circle?

Question 3

In which of the circles is the segment drawn the radius?

**Query**

Given a circle whose circumference $6.28$

What is the area?

**Solution**

To solve this question we will use two formulas:

The first formula is to calculate the circumference:

$P=2×π×R$

$3.14=pi\times R$

We divide by $(3.14)$

$R=1$

The second formula is for calculating the area of the circle

$A=π×R×R$

We replace the answer we got

$A=π×1×1$

$A=π$

**Answer**

$π$

**Request**

Given the shape of the figure

A quadrilateral is a square with the length of its sides $5\operatorname{cm}$

For each side extends a semicircle.

What is the circumference of this shape?

**Solution**

The circumference consists of $4$ semicircles.

$4\cdot\frac{1}{2}p=2p$

That is, in total $2$ circumference than its diameter $5\operatorname{cm}$

Diameter = Radius multiplied by $2$

The radius multiplied by $2=5$

Divide by $2$

$radio=2.5 cm$

$p=2\pi\cdot2.5=5\pi$

We calculate the area of the form

$2\cdot p=2\cdot5\pi=10\pi$

**Answer**

$10\pi$

Test your knowledge

Question 1

Is it correct to say:

'the circumference of a circle'?

Question 2

Where does a point need to be so that its distance from the center of the circle is the shortest?

Question 3

The number Pi \( (\pi) \) represents the relationship between which parts of the circle?

**Request**

Given the shape of the figure

For the sides of the triangle two semicircles are extended.

The triangle is equilateral and each side has a length of $6X\operatorname{cm}$

What is the circumference of the shape?

**Solution**

$P=ladotriángulo+2\cdot\left(\frac{1}{2}P\right)$

Diameter of the circle

= $6X\operatorname{cm}$

Each semicircle contributes to the circumference of the semicircle of the whole circle the diameter of one side of a triangle.

$p=6x+2\cdot(\frac{1}{2}\cdot2\pi r)=$

We reduce by : $2$

$6x+2\cdot\pi(\frac{6x}{2})=$

We reduce by: $2$

$6x+6\pi x$

**Answer**

$6x+6\pi x$

**Request**

Given the circle in the figure

The radius of the circle is equal to: $9.5$

What is its circumference?

**Solution**

The radius of the circle is $r=9\frac{1}{2}$

We use the formula of the circumference

$2\pi r$

We replace accordingly and get

$2\cdot\pi\cdot9\frac{1}{2}=19\pi$

**Answer**

$19\pi$

Do you know what the answer is?

Question 1

M is the center of the circle.

In the figure we observe 3 diameters?

Question 2

Is there sufficient data to determine that

\( GH=AB \)

Question 3

M is the center of the circle.

Perhaps \( MF=MC \)

**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:

$S_1=7\cdot8-4\cdot\pi(\frac{2}{2})^2=$

$56-4\pi(\frac{2}{2})^2=43.44$

$S_2=9\cdot20-3\cdot\pi(\frac{3}{2})^2=$

$9\cdot20-3\pi(\frac{3}{2})^2=$

$9\cdot20-6.75\pi=158.805$

**Answer**

$B$

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

M is the center of the circle.

Perhaps \( AB=CD \)

Question 2

Which diagram shows a circle with a point marked in the circle and not on the circle?

Question 3

Which figure shows the radius of a circle?

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.

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

Is it correct to say the area of the circumference?

Question 2

All ____ about the circle located in the distance ____ from the ____ circle

Question 3

In which of the circles is the center of the circle marked?

That which has a radius equal to $1$ is called a unit circle.

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 $A=\pi R^2$

Let's see an example:

**Assignment:**

Calculate the area of the following circle with $D=9\text{ cm}$

We know that the radius is half the diameter, therefore:

$R=4.5\text{ cm}$

$\pi=3.14$

Now we substitute this data into the area formula:

$A=\pi R^2=3.14\left(4.5\text{ cm} \right)^2$

$3.14\left(20.25\operatorname{cm}^2 \right)=63.585\operatorname{cm}^2$

**Answer**

$A=63.585\operatorname{cm}^2$

Test your knowledge

Question 1

In which of the circles is the point marked in the circle and not on the circumference?

Question 2

Which diagram shows the radius of a circle?

Question 3

In which of the circles is the segment drawn the radius?

Which figure shows the radius of a circle?

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.

Which diagram shows a circle with a point marked in the circle and not on the circle?

The interpretation of "in a circle" is inside the circle.

In diagrams a'-d' the point is on the circle, and in diagram c' the point is outside the circle.

M is the center of the circle.

Perhaps $AB=CD$

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:

$AB\ne CD$

No

A point whose distance from the center of the circle is _______ than the radius, is outside the circle.

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.

greater

Where does a point need to be so that its distance from the center of the circle is the shortest?

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 less than the radius from the center of the circle will necessarily be inside the circle.

Inside

Related Subjects

- Area
- Trapezoids
- Area of a trapezoid
- Perimeter of a trapezoid
- Parallelogram
- The area of a parallelogram: what is it and how is it calculated?
- Perimeter of a Parallelogram
- Elements of the circumference
- Circle
- Diameter
- Pi
- Area of a circle
- Distance from a chord to the center of a circle
- Chords of a Circle
- Central Angle in a Circle
- Arcs in a Circle
- Perpendicular to a chord from the center of a circle
- Inscribed angle in a circle
- Tangent to a circle
- The Circumference of a Circle
- The Center of a Circle
- Radius
- How is the radius calculated using its circumference?
- Rectangle
- Calculating the Area of a Rectangle
- The perimeter of the rectangle
- Perimeter
- Triangle
- The Area of a Triangle
- Area of a right triangle
- Area of Isosceles Triangles
- Area of a Scalene Triangle
- Area of Equilateral Triangles
- Perimeter of a triangle
- Cylinder Area
- Cylinder Volume