- Math Article
Circles in Maths
In Maths or Geometry, a circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the centre. The distance from the centre of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
A circle is a basic 2D shape which is measured in terms of its radius. The circles divide the plane into two regions such as interior and exterior region. It is similar to the type of line segment. Imagine that the line segment is bent around till its ends join. Arrange the loop until it is precisely circular.
The circle is a two-dimensional figure, which has its area and perimeter. The perimeter of the circle is also called the circumference, which is the distance around the circle. The area of the circle is the region bounded by it in a 2D plane. Let us discuss here circle definition, formulas, important terms with examples in detail.
Table of Contents:
- How to Draw Circle
- Area and Circumference
- Circle Proof
Practice Problems
Circle definition.
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle. The circle formula in the plane is given as:
(x-h) 2 + (y-k) 2 = r 2
where (x,y) are the coordinate points (h,k) is the coordinate of the centre of a circle and r is the radius of a circle.
Circle Shaped Objects
There are many objects we have seen in the real world that are circular in shape. Some of the examples are:
We can observe many such examples in our day to day life.
How to Draw a Circle?
In maths projects for class 10 on circles, the construction of a circle, all the properties and terminologies are explained in detail. To understand what circles are in simple terms, go through circles for class 10 , and also try the following exercise –
- Take an empty sheet of paper and mark a single point on the sheet, somewhere in the middle of the sheet, and name it to point O.
- Select a random length for radius, for example, 3 cm.
- Using a ruler, keep the reference zero mark on point O and randomly mark 3 cm away from point O in all the direction.
- Mark as many points as you want away from point O, but all of them should be exactly 3 cm away from point O.
If you’ve selected sufficient points, you may notice that the shape is starting to resemble a circle and this is exactly what the definition of a circle is.
Parts of Circle
A circle has different parts based on the positions and their properties. The different parts of a circle are explained below in detail.
- Annulus- The region bounded by two concentric circles. It is basically a ring-shaped object. See the figure below.
- Arc – It is basically the connected curve of a circle.
- Sector – A region bounded by two radii and an arc.
- Segment- A region bounded by a chord and an arc lying between the chord’s endpoints. It is to be noted that segments do not contain the centre.
See the figure below explaining the arc, sector and segment of a circle.
- Centre – It is the midpoint of a circle.
- Chord- A line segment whose endpoints lie on the circle.
- Diameter- A line segment having both the endpoints on the circle and is the largest chord of the circle.
- Radius- A line segment connecting the centre of a circle to any point on the circle itself.
- Secant- A straight line cutting the circle at two points. It is also called an extended chord.
- Tangent- A coplanar straight line touching the circle at a single point.
See the figure below-representing the centre, chord, diameter, radius, secant and tangent of a circle.
Radius of Circle (r)
A line segment connecting the centre of a circle to any point on the circle itself “. The radius of the circle is denoted by “R” or “r”.
Diameter (d) of Circle
A line segment having both the endpoints on the circle. It is twice the length of radius i.e. d = 2r . From the diameter, the radius of the circle formula is obtained as r= d/2.
Also, read:
Circle Formulas
We know that a circle is a two-dimensional curve-shaped figure, and the two different parameters used to measure the circle are:
- Area of circle
- Circumference of a circle
Let us discuss here the general formulas for area and perimeter/ circumference of a circle .
Area and Circumference of a Circle
Circle area proof.
We know that Area is the space occupied by the circle.
Consider a concentric circle having an external circle radius to be ‘r.’
Open all the concentric circles to form a right-angled triangle.
The outer circle would form a line having length 2πr forming the base.
The height would be ‘r’
Therefore the area of the right-angled triangle formed would be equal to the area of a circle.
Area of a circle = Area of triangle = (1/2) × b × h
= (1/2) × 2π r × r
Therefore, Area of a circle = πr 2
Properties of Circles
The important basic properties of circles are as follows:
- The outer line of a circle is at equidistant from the centre.
- The diameter of the circle divides it into two equal parts.
- Circles which have equal radii are congruent to each other.
- Circles which are different in size or having different radii are similar.
- The diameter of the circle is the largest chord and is double the radius.
Video Lessons on Circles
Circles – one shot revision.
Introduction to Circles
Parts of a Circle
Area of a Circle
All about Circles
Solved Examples
Find the area and the circumference of a circle whose radius is 10 cm. (Take the value of π = 3.14 )
Given: Radius = 10 cm.
Area =π r 2
= 3.14 × 10 2
A= 314 cm 2
Circumference, C = 2πr
C= 2 ×3.14× 10
Circumference= 62.8 cm
Example 2:
Find the area of a circle whose circumference is 31.4 cm.
Circumference = 31.4 cm
To find the area of a circle, we need to find the radius.
From the circumference, the radius can be calculated:
2 π r = 31.4
(2)(3.14)r = 31.4
r = 31.4 /(2)(3.14)
Therefore, the radius of the circle is 5 cm.
The area of a circle is πr 2 square units
Now, substitute the radius value in the area of a circle formula, we get
A = 3.14 x 25
A = 78.5 cm 2
Therefore, the area of a circle is 78.5 cm 2 .
Solve the following circle problems given below:
- Find the area of a circle whose radius is 7 cm
- Find the circumference of a circle whose radius is 9 cm
- The area of a circle is 176 cm 2 . Find its radius
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Frequently Asked Questions on Circles
What is called a circle.
A circle is a closed two-dimensional curve shaped figure, where all the points on the surface of the circle are equidistant from the centre point.
What are the different parts of a circle?
The different parts of a circle are radius, diameter, chord, tangent, arc, centre, secant, sector.
Write down the circle formulas.
If “r” is the radius of the circle, then the formula for the area and the circumference of a circle are: Circumference of a Circle = 2πr units Area of a circle = πr 2 square units.
Define radius and diameter of a circle.
Define chord.
Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!
Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz
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how to calculate chord length of circle
Formula to calculate Chord Length of a circle = 2 × √(r power 2 − d power 2). Kindly check our chord of a circle page – https://byjus.com/maths/chord-of-circle/
by applying the formula of circumference i think so.
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- Lesson 7.1 Introduction to Circles
LESSON VIDEOS
Introduction to Circles >>
Introduction to Completing the Square >>
Notes 7.1 >>
HOMEWORK VIDEOS
- Lesson 7.2 Converting Circles to Descriptive Form
- Lesson 7.3 Definition of a Parabola from the Focus & Directrix
- Lesson 7.4 Sideways Parabolas from the Focus & Directrix
- Lesson 7.5 Transformations of Parabolas
- Lesson 7.6 Converting Parabolas from General to Descriptive Form
- Lesson 7.7 Converting Parabolas and Circles to Descriptive Form
- Unit 7 Review
- Worksheet 7.1 >>
KHAN ACADEMY:
- Features of a Circle from its Standard Equatio n
- Graphing a Circle from its Standard Equation
- Completing the Square
PURPLE MATH:
- Circles: Introduction & Drawing
- Solving Quadratic Equations: Solving by Completing the Square
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Introduction to Circles Assignment 5.0 (3 reviews) Which circle C shows a chord that is not a diameter? Click the card to flip 👆 D Click the card to flip 👆 1 / 10 Flashcards Learn Test Match Q-Chat HaileyC771 Top creator on Quizlet Students also viewed Introduction to Circles: Quiz 10 terms macwhite04 Preview Introduction to Circles 13 terms
What is AC? Secant Tangent Secant Radius Circle A has a radius of 6. Which circles are congruent to circle A? Check all that apply. circle D circle E circle F circle G circle H E & F Complete the statements about circle Z. A central angle, such as angle ___of circle Z, is an angle whose vertex is Angle____ is not a central angle of circle Z.
Central Angles Assignment. 10 terms. HaileyC771. Preview. Introduction to Circles Quiz. 10 terms. Sarcxstic. Preview. Geometry HN Unit 6 (second half) 7 terms. LindsayyyK. Preview. Classifying Angles. Teacher 13 terms. ... Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown.
A circle is the set of all points equidistant from a given point. The point from which all the points on a circle are equidistant is called the center of the circle, and the distance from that point to the circle is called the radius of the circle. A circle is named with a single letter, its center. See the diagram below. Figure %: A circle
Determining tangent lines: lengths. Proof: Segments tangent to circle from outside point are congruent. Tangents of circles problem (example 1) Tangents of circles problem (example 2) Tangents of circles problem (example 3) Challenge problems: radius & tangent. Challenge problems: circumscribing shapes.
What is the radius of the circle formed by the seeds Miguel is spitting in his backyard? Explain your reasoning. g. What is the diameter of the circle formed by the seeds Miguel is spitting in the backyard? Explain your reasoning. 7718A_C2_Assign_CH12_221-236.indd 222 6/14/11 10:02 AM
circle. diameter. radius. the set of all points in a plane that are equidistant from a given point. a segment that extends from the center of a circle to any point on the circle. a segment with both endpoints on a circle. a chord that passes through the center of the circle. Defining a Circle.
will map circle A onto circle B, then the circles are _____. How can similarity transformations be used to prove that all circles are similar? • _____ circle A so that _____ A maps onto center B, creating concentric circles, or circles that have the same center but different radii. transformations similar Translate center
Eventually, Noah realizes that this assignment was NOT a geometry construction mathplane.com . Parts of a circle. Sector: An area inside the circle bounded by 2 radii and an arc. ... Introduction to Circles: Test radius is 3 units Arc B is a semi-circle Portion: 1 Area of entire circle: center of circle: (4, 4) Sector area:
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called "centre". Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle. The circle formula in the plane is given as:
Study with Quizlet and memorize flashcards containing terms like In the bull's-eye shown above, AB = BC = CD = DE, and AB = 3 in. Calculate the area of the outer black ring of the bull's-eye. Round the answer to the nearest tenth. A. 18.8 in.² B. 28.3 in.² C. 63.0 in.² D. 197.9 in.², Find the circumference of the larger circle if the area of one of the smaller circles is 48 π in², Find ...
Solve the Test Item. The radius of the circle is the same as the hypotenuse of the right triangle. In a 30°-60°-90°, the hypotenuse is twice the length of the shorter leg, which is opposite the 30° angle. Since the side opposite the 30° angle measures 15 cm, the hypotenuse measures 30 cm. So, the diameter of the circle is 60 cm.
Introduction to Circles (Students Study Material & Assignment) - Free download as PDF File (.pdf), Text File (.txt) or read online for free. This should be able to solve simple problems involving the equation of a circle.
Introduction to Circles Loading... Image Attributions Show Details Show Resources Introduces the features of circles including secant, secant line, chord, diameter, radius, tangent line, and intersecting circles.
Lesson 7.1 Introduction to Circles; Lesson 7.2 Converting Circles to Descriptive Form; Lesson 7.3 Definition of a Parabola from the Focus & Directrix; Lesson 7.4 Sideways Parabolas from the Focus & Directrix; Lesson 7.5 Transformations of Parabolas; Lesson 7.6 Converting Parabolas from General to Descriptive Form
Math Courses / Math 97: Introduction to Mathematical Reasoning Course / Introduction to Circles Chapter Introduction to Circles Chapter Exam Free Practice Test Instructions:
A tangent is never a secant. 4. A chord can be longer than a diameter of the same circle. 5. A chord can be shorter than a radius of the same circle. 6. A radius is always congruent to another radius of the same circle. 2. A diameter is always a chord.
$3.00 4.8 (46) PDF Add one to cart Intro to Circles Exploration Activity | Circumference & Diameter Activity Created by Maneuvering the Middle This Circumference of Circles Introductory Activity allows students to work collaboratively and explore the relationship between circumference and diameter using models.
Introduction. Call your students together as a group, and ask them if they can identify a circle. Inform students that they will sing one verse of "The Wheels on the Bus," and do the actions. Altogether, sing: The wheels on the bus go round and round, round and round, round and round, the wheels on the bus go round and round, all through the town.
Introduction to circles 3.5 (2 reviews) Andy wants to build a circular concrete patio in his backyard and install a jungle gym on top of it. One 80-lb bag of concrete will be enough for 2 square feet. If he wants the diameter of the patio to be 10 ft, how many bags of concrete will he need to purchase? Click the card to flip 👆 B
Doc Preview 4. A fellow student asks, "Are all circles similar?" What is your answer to this question? Be sure to provide support for your answer. Now we will introduce some notation and terminology needed to study circles.
Introduction to Circles The set of all points in a plane that are equidistant from a point in the same plane. Click the card to flip 👆 Circle Click the card to flip 👆 1 / 20 Flashcards Learn Test Match Created by anika_basu Terms in this set (20) The set of all points in a plane that are equidistant from a point in the same plane. Circle
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