Which figure shows the radius of a circle?

Parts of Circle Practice Problems - Center, Radius & Diameter

Master circle parts with step-by-step practice problems. Learn to identify center, calculate radius, diameter, circumference and area with worked examples.

📚What You'll Master in Circle Parts Practice

Identify and locate the center point of any circle or circumference
Calculate radius from diameter and diameter from radius measurements
Find circumference using the formula 2πr with given radius values
Determine circle area using πr² formula from radius or diameter
Solve complex problems involving concentric circles and inscribed shapes
Apply circle formulas to real-world geometry problems and word problems

Understanding The Center of a Circle

Complete explanation with examples

The center of the circumference belongs to subtopics that make up the topic of the circumference and the circle. We use the concept of the center of the circumference to define the circumference itself, as well as to calculate the radius and diameter of each given circumference.

The center of the circumference, as its name indicates, is a point located in the center of the circumference. It is usually customary to mark this point with the letter O. Indeed, this point is at the same distance from each of the points that make up the circumference.

Detailed explanation

Practice The Center of a Circle

Test your knowledge with 11 quizzes

True or false:

The radius of a circle is the chord.

Examples with solutions for The Center of a 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

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

Exercise #3

The number Pi $(\pi)$ represents the relationship between which parts of the circle?

Step-by-Step Solution

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:

C = \pi \times d

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

Answer:

Perimeter and diameter

Exercise #4

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:

Video Solution

Exercise #5

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:

Frequently Asked Questions

Everything you need to know about The Center of a Circle

What is the center of a circle and how do I find it?

The center of a circle is the point that is equidistant from all points on the circumference. It's typically marked with the letter O and serves as the reference point for measuring radius and diameter. In problems, the center is either given or can be found as the midpoint of a diameter.

How do you calculate the circumference of a circle?

Use the formula C = 2πr, where r is the radius. If you're given the diameter instead, you can use C = πd. For example, if the radius is 4 cm, then C = 2π(4) = 8π cm.

What's the difference between radius and diameter of a circle?

The radius is the distance from the center to any point on the circle's edge. The diameter is twice the radius and represents the distance across the entire circle through the center. Formula: d = 2r or r = d/2.

How do I find the area of a circle step by step?

Follow these steps: 1) Identify the radius (if given diameter, divide by 2), 2) Square the radius value, 3) Multiply by π using the formula A = πr². For example, if r = 5, then A = π(5)² = 25π square units.

What are the main parts of a circle I need to know?

Key circle parts include: Center (point O equidistant from circumference), Radius (line from center to edge), Diameter (line through center connecting two points), Chord (line connecting two points), and Circumference (the circle's perimeter).

How do you solve problems with circles inside circles?

For concentric circles (same center), find each circle's area separately using A = πr², then subtract the smaller from the larger for the ring area. Always identify the radius of each circle first, then apply the appropriate formulas.

What happens if a circle has radius zero?

If the radius equals zero, there is no actual circle - just a single point. Since radius defines the distance from center to circumference, a zero radius means no circumference exists, resulting in no measurable area or perimeter.

How do I solve word problems involving circle measurements?

Read carefully to identify what's given (radius, diameter, or circumference) and what you need to find. Draw a diagram if helpful, then choose the appropriate formula: C = 2πr for circumference, A = πr² for area, or d = 2r for diameter relationships.

Continue Your Math Journey

Master The Center of a 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 Radius How is the radius calculated using its circumference?Perimeter Parts of a Circle Area Elements of the circumference Area of a circle

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Calculating the size Determine whether or not it is possible to draw Identifying and defining elements True / false Value of Pi