The Center of a Circle - Examples, Exercises and Solutions

To solve this problem, we will consider the parts of a circle and how they interplay based on the description provided in the incomplete sentence:

• Step 1: Recognize that the first blank needs a term that refers to the primary element defining a circle externally.
• Step 2: The second blank needs a term associated with 'equal' as it describes distances from a specific location, hinting at a property of circles.
• Step 3: The third blank likely wants us to relate this location to the circle itself, denoting the standard geometric reference point.

Now, let's fill in each blank systematically:

The first term 'Point' refers to all points lying on the perimeter of a circle. In the definition of a circle, each point on the circle’s circumference maintains an equal distance from its center.

The second term 'equal' pertains to how all these points are at an equal distance - which is the radius - from the center.

The third term 'center' specifies the reference point within the circle from which every point on the circle is equidistant.

Thus, the complete statement is: "All point about the circle located in the distance equal from the center circle."

The correct choice that completes the sentence is: Point, equal, center.

To determine if the statement "If the radius of a circle is 5 cm, then the length of the diameter is 10 cm" is true, we need to use the relationship between the radius and diameter of a circle.

The diameter $d$ of a circle is calculated using the formula:

$d = 2r$

where $r$ is the radius. In this problem, the radius $r$ is given as 5 cm.

Using the formula, the diameter is:

$d = 2 \times 5 \, \text{cm} = 10 \, \text{cm}$

This matches exactly the length of the diameter given in the problem.

Therefore, the statement "If the radius of a circle is 5 cm, then the length of the diameter is 10 cm" is True.

To solve this problem, we will clarify the relationship between the constant $\pi$ and parts of a circle.

The number $\pi$ is a constant that relates the circumference of a circle (the perimeter) to its diameter. The formula for the circumference $C$ of a circle is given by:

where $C$ is the circumference, and $d$ is the diameter of the circle. This equation shows that $\pi$ is the ratio of the circumference of a circle to its diameter, which remains constant for all circles.

Therefore, $\pi$ indeed represents the relationship between the circle’s perimeter and its diameter.

Thus, the correct answer is: Perimeter and diameter

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.

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.

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.

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:

$AB\ne CD$

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.