# The Center of a Circle - Examples, Exercises and Solutions

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.

## Examples with solutions for The Center of a Circle

### Exercise #1

M is the center of the circle.

Perhaps $AB=CD$

### 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:

$AB\ne CD$

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.

False

### Exercise #3

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.

### Exercise #4

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

### Exercise #5

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

### Step-by-Step Solution

To calculate, we will use the formula:

$\frac{P}{2r}=\pi$

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:

$\frac{8}{4}=\pi$

$2\ne\pi$

Therefore, this situation is not possible.

Impossible

### Exercise #6

M is the center of the circle.

Perhaps $MF=MC$

Yes

### Exercise #7

M is the center of the circle.

In the figure we observe 3 diameters?

No

### Exercise #8

Is there sufficient data to determine that

$GH=AB$

No

### Exercise #9

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

### Exercise #10

Perhaps $P=\pi\times EF$

Yes

### Exercise #11

M is the center of the circle.

Perhaps $CM+MD=2EM$

Yes

### Exercise #12

M is the center of the circle.

Is AB the diameter?

No

### Exercise #13

Perhaps $MF+MD=AB$

No

### Exercise #14

M is the center of the circle.

Perhaps $0.5DC=EM$

Yes

### Exercise #15

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