Parts of the Circle: Identifying and defining elements

Examples with solutions for Parts of the Circle: Identifying and defining elements

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:

ABCD AB\ne CD

Answer

No

Exercise #2

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

Answer

Exercise #4

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

2π 2\ne\pi

Therefore, this situation is not possible.

Answer

Impossible

Exercise #5

M is the center of the circle.

Perhaps MF=MC MF=MC

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

Yes

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

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

Video Solution

Answer

Exercise #9

Perhaps P=π×EF P=\pi\times EF

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

Yes

Exercise #10

M is the center of the circle.

Perhaps CM+MD=2EM CM+MD=2EM

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

Yes

Exercise #11

M is the center of the circle.

Is AB the diameter?

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

No

Exercise #12

Perhaps MF+MD=AB MF+MD=AB

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

No

Exercise #13

M is the center of the circle.

Perhaps 0.5DC=EM 0.5DC=EM

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

Yes

Exercise #14

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 #15

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 #16

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 #17

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

Video Solution

Answer

No.

Exercise #18

M is the center of the circle.

Perhaps AB+GH<4\times CM MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

Yes

Exercise #19

M is the center of the circle.

Perhaps EM+MC>AB

MMMAAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Answer

Yes