# Diameter - Examples, Exercises and Solutions

A diameter is a section that connects two points that lie on the circumference, that passes through the center of the circle. The diameter is actually twice the radius.

As in the case of the radius, as well as in the case of the diameter, there are an infinite number of diameters on the circumference, and all are identical in length.

Below is an example of a circle with several diameters marked in different colors.

## Examples with solutions for Diameter

### 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.

Therefore, the answer is incorrect, as there are infinite radii.

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?

No.