The Center of a Circle - Examples, Exercises and Solutions

Question Types:
Parts of the Circle: Value of PiParts of the Circle: Determine whether or not it is possible to drawParts of the Circle: Calculating the sizeParts of the Circle: Identifying and defining elements

The center of the circumference belongs to subtopics that make up the topic of the circumference and the circle. We use the concept of the center of the circumference to define the circumference itself, as well as to calculate the radius and diameter of each given circumference.

The center of the circumference, as its name indicates, is a point located in the center of the circumference. It is usually customary to mark this point with the letter O. Indeed, this point is at the same distance from each of the points that make up the circumference.

P1 - The center of the circumference

Detailed explanation

Practice The Center of a Circle

Question 1

M is the center of the circle.

Perhaps \( AB=CD \)

MMMAAABBBCCCDDDEEEFFFGGGHHH

Question 2

There are only 4 radii in a circle.

Question 3

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

Question 4

Which figure shows the radius of a circle?

Question 5

Is it possible that the circumference of a circle is 8 meters and its diameter is 4 meters?

Examples with solutions for The Center of a Circle

Exercise #1

M is the center of the circle.

Perhaps AB=CD AB=CD

MMMAAABBBCCCDDDEEEFFFGGGHHH

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 AB\ne CD

Answer

No

Exercise #2

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 #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

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 #5

Is it possible that the circumference of a circle is 8 meters and its diameter is 4 meters?

Video Solution

Step-by-Step Solution

To calculate, we will use the formula:

P2r=π \frac{P}{2r}=\pi

Pi is the ratio between the circumference of the circle and the diameter of the circle.

The diameter is equal to 2 radii.

Let's substitute the given data into the formula:

84=π \frac{8}{4}=\pi

2≠π 2\ne\pi

Therefore, this situation is not possible.

Answer

Impossible

Question 1

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

Question 2

Is there sufficient data to determine that

\( GH=AB \)

MMMAAABBBCCCDDDEEEFFFGGGHHH

Question 3

M is the center of the circle.

In the figure we observe 3 diameters?

MMMAAABBBCCCDDDEEEFFFGGGHHH

Question 4

M is the center of the circle.

Perhaps \( MF=MC \)

MMMAAABBBCCCDDDEEEFFFGGGHHH

Question 5

Fill in the corresponding sign

\( \pi?3.147 \)

Exercise #6

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

Video Solution

Answer

Exercise #7

Is there sufficient data to determine that

GH=AB GH=AB

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

No

Exercise #8

M is the center of the circle.

In the figure we observe 3 diameters?

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

No

Exercise #9

M is the center of the circle.

Perhaps MF=MC MF=MC

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

Yes

Exercise #10

Fill in the corresponding sign

π?3.147 \pi?3.147

Video Solution

Answer

= =

Question 1

Fill in the corresponding sign

\( \pi?3.2 \)

Question 2

Is it possible for a circle to have a circumference of 314.159 meters (approximately) and a diameter of 100 meters?

Question 3

Is it possible for the circumference of a circle to be \( 10\pi \) if its diameter is \( 2\pi \) meters?

Question 4

Is it possible for the circumference of a circle to be \( 5\pi \) meters if its diameter 5 meters?

Question 5

Is it possible that a circle with a circumference of 50.6 meters has a diameter of 29 meters?

Exercise #11

Fill in the corresponding sign

π?3.2 \pi?3.2

Video Solution

Answer

<

Exercise #12

Is it possible for a circle to have a circumference of 314.159 meters (approximately) and a diameter of 100 meters?

Video Solution

Answer

No.

Exercise #13

Is it possible for the circumference of a circle to be 10π 10\pi if its diameter is 2π 2\pi meters?

Video Solution

Answer

No.

Exercise #14

Is it possible for the circumference of a circle to be 5π 5\pi meters if its diameter 5 meters?

Video Solution

Answer

No.

Exercise #15

Is it possible that a circle with a circumference of 50.6 meters has a diameter of 29 meters?

Video Solution

Answer

No.

Topics learned in later sections

  1. Circle
  2. Diameter
  3. Pi
  4. The Circumference of a Circle
  5. Radius
  6. How is the radius calculated using its circumference?
  7. Perimeter
  8. Area
  9. Elements of the circumference
  10. Area of a circle