Circle - Examples, Exercises and Solutions

Understanding Circle

Complete explanation with examples

Circle

A circle is a two-dimensional shape where every point on the boundary is equidistant from a central point, called the center. The circle is actually the inner part of the circumference, i.e., the enclosed area inside the circle frame. This distance between the boundary and the center is called radius. The diameter is twice the radius, and it passes through the center, dividing the circle into two equal parts.

Below are some examples of circles with different circumferences. The colored part in each represents the circle:

examples of circles with different circumferences.
More relevant components of the circle:
  • Radius: The distance from the center of the circle to any point on the circumference.
  • Diameter: A straight line passing through the center that connects two points on the circumference, equal to twice the radius.
  • Arc: A portion of the circumference.
  • Chord: A line segment connecting two points on the circle.
  • Tangent: A line that touches the circle at exactly one point.

Circumference

The perimeter or boundary length of the circle.
Can be calculated as: C=2πrC=2\pi r

Area

he space enclosed within the circle, calculated as A=πr2A = \pi r^2

Detailed explanation

Practice Circle

Test your knowledge with 17 quizzes

The diameter of a circle is twice as long as its radius.

Examples with solutions for 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 AB=CD

MMMAAABBBCCCDDDEEEFFFGGGHHH

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≠CD 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

A point whose distance from the center of the circle is _______ than the radius, is outside the circle.

Step-by-Step Solution

Let's remember that the circle is actually the inner part of the circumference, meaning the enclosed area within the frame of the circumference.

Therefore, a point whose distance is greater than the center of the circle will necessarily be outside the circle.

Answer:

greater

Exercise #5

Where does a point need to be so that its distance from the center of the circle is the shortest?

Step-by-Step Solution

Let's remember that the circle is actually the inner part of the circumference, meaning the enclosed area within the frame of the circumference.

Therefore, a point whose distance is less than the radius from the center of the circle will necessarily be inside the circle.

Answer:

Inside

More Circle Questions

Click on any question to see the complete solution with step-by-step explanations

Parts of the Circle

True or False: Is the Radius of a Circle a Chord? Circle Geometry Proof: Demonstrating Infinite Diameters in a Circle Circle Diameter Definition: Points, Center, and Line Segments

The Parts of a Circle

Solve Circle Equation x²-8ax+y²+10ay=-5a² Using Completing Square Method Complete the Square for x²-6x+y²-4y=7: Find Circle's Center & Radius

Continue Your Math Journey

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

Topics Learned in Later Sections

DiameterPiThe Circumference of a CircleThe Center of a CircleRadiusHow is the radius calculated using its circumference?PerimeterParts of a CircleAreaElements of the circumferenceArea 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 Calculate the ratio between radii of two circles Calculating arc length Calculating parts of the circle Identifying and defining elements