Diameter - Examples, Exercises and Solutions

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.

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

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:

$AB\ne CD$

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.