Parts of the Circle - Examples, Exercises and Solutions

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

Parts of a Circle

Circle radius

The radius is the distance from the center point of the circle to any point on its circumference, it is denoted by RR and it equals half the diameter.

The diameter of the circle

The diameter is a straight line that passes through the center point of the circle and connects 22 points on the circumference. The diameter equals twice the radius.

Pi

Pi is a constant number that represents the ratio between a circle's circumference and its diameter.
Its symbol is ππ and it is always equal to 3.143.14.

perpendicular

A perpendicular is a straight line that extends from the center of the circle to any chord in the circle, divides the chord into 22 equal parts, creates 22 right angles with the chord, and bisects the arc corresponding to the chord.

Circle diagram illustrating key geometric components including a radius, chord, and right triangle inscribed within the circle. Ideal for learning parts of a circle, radius, diameter, and perpendicular relationships in geometry.

MM - center of the circle
RR - radius of the circle
KK - diameter of the circle
Blue line - chord
Orange line - perpendicular

Detailed explanation

Practice Parts of the Circle

Question 1

There are only 4 radii in a circle.

Question 2

M is the center of the circle.

Perhaps \( AB=CD \)

MMMAAABBBCCCDDDEEEFFFGGGHHH

Question 3

Which figure shows the radius of a circle?

Question 4

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

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 #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.

Answer

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) and (d) the point is on the circle, while in diagram (c) the point is outside of the circle.

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

M is the center of the circle.

In the figure we observe 3 diameters?

MMMAAABBBCCCDDDEEEFFFGGGHHH

Question 2

Is there sufficient data to determine that

\( GH=AB \)

MMMAAABBBCCCDDDEEEFFFGGGHHH

Question 3

M is the center of the circle.

Perhaps \( MF=MC \)

MMMAAABBBCCCDDDEEEFFFGGGHHH

Question 4

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

Question 5

Fill in the corresponding sign

\( \pi?3.2 \)

Exercise #6

M is the center of the circle.

In the figure we observe 3 diameters?

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

No

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.

Perhaps MF=MC MF=MC

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

Yes

Exercise #9

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

Video Solution

Answer

Exercise #10

Fill in the corresponding sign

π?3.2 \pi?3.2

Video Solution

Answer

<

Question 1

Fill in the corresponding sign

\( \pi?3.147 \)

Question 2

M is the center of the circle.

Is AB the diameter?

MMMAAABBBCCCDDDEEEFFFGGGHHH

Question 3

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

Question 4

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

Question 5

M is the center of the circle.

Perhaps \( 0.5DC=EM \)

MMMAAABBBCCCDDDEEEFFFGGGHHH

Exercise #11

Fill in the corresponding sign

π?3.147 \pi?3.147

Video Solution

Answer

<

Exercise #12

M is the center of the circle.

Is AB the diameter?

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

No

Exercise #13

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

Video Solution

Answer

No.

Exercise #14

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 #15

M is the center of the circle.

Perhaps 0.5DC=EM 0.5DC=EM

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

Yes

Topics learned in later sections

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