Parts of the Circle - Examples, Exercises and Solutions

Understanding Parts of the Circle

Complete explanation with examples

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 $R$ 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 $2$ 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 $π$ and it is always equal to $3.14$ .

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 $2$ equal parts, creates $2$ 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.

$M$ - center of the circle
$R$ - radius of the circle
$K$ - diameter of the circle
Blue line - chord
Orange line - perpendicular

Detailed explanation

Practice Parts of the Circle

Test your knowledge with 11 quizzes

True or false:

The radius of a circle is the chord.

Examples with solutions for Parts of the Circle

Step-by-step solutions included

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 $AB=CD$

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:

$AB\ne CD$

Answer:

No

Video Solution

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

If the radius of a circle is 5 cm, then the length of the diameter is 10 cm.

Step-by-Step Solution

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.

Answer:

True

Continue Your Math Journey

Master Parts of the Circle first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Circle Diameter Pi The Circumference of a Circle The Center of a Circle Radius How is the radius calculated using its circumference?Perimeter Area Elements of the circumference Area of a circle

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