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24 Jul 2019, 01:06
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Properties of Circles
Purpose of the article:
Hello Reader,
We see that you want to know the basics of circles.
- • You have landed just at the right place.
In this article,
- • You will get an idea about circles and the related terms.
• You will also get to know about the properties of circles.
Circle- Definition
When all points that are at a fixed distance from a fixed point are joined, the geometrical figure obtained is called a circle.
Let us now learn a bit about the terminology used in circles.
Terms related to Circles
1- Center
The fixed point in the circle is called the center.
- • So, the set of points are at a fixed distance from the center of the circle.
2- Radius
Radius is the fixed distance between the center and the set of points. It is denoted by “R.”
3- Diameter
Diameter is a line segment, having its endpoints on the circle and passing through the center.
- • So, logically, a diameter can be broken into two parts:
- o One part from one endpoint of the diameter to the center of the circle
o And, the other part from the center of the circle to another endpoint of the diameter.
- Hence, Diameter = Twice the length of the radius or “D= 2R.”
4- Circumference
It is the measure of the outside boundary of the circle.
• So, the length of the circle or the perimeter of the circle is called circumference.
5- Arc
An arc is a portion of the circle’s circumference.
From any two-point that lie on the boundary of the circle, two arcs can be created: A Minor and a Major Arc.
• Minor arc: The shortest arc created by two points.
• Major Arc: The longest arc created by two points.
6- Sector
A sector is formed by joining the endpoints of an arc with the center.
- • On joining the endpoints with the center, two sectors will be obtained: Minor and Major.
- o By default, we only consider the Minor sector unless it is mentioned otherwise.
7- Semi-circle
A semi-circle is half part of the circle or,
• A semi-circle is obtained when a circle is divided into two equal parts.
Now that we know all the terminologies related to circles, let us learn about the properties of circles.
Important Properties Related to lines in a circle
1- Chord
A chord is a line segment whose endpoints lie on the boundary of the circle.
Properties of Chord
Perpendicular dropped from the center divides a chord into two equal parts.
2 - Tangent
A tangent is a line that touches the circle at any one point.
Properties of Tangent
Radius is always perpendicular to the tangent at the point where it touches the circle.
Important Properties Related to angles in a circle
1- Inscribed Angle
An inscribed angle is the angle formed between two chords when they meet on the boundary of the circle.
Properties of Inscribed Angle
1- All the angles formed by an arc on the circumference of the circle are always equal.
2- Angle in a semi-circle is always 900.
3- Central Angle
A central angle is the angle formed when two-line segments meet such that one of the endpoints of both the line segment is at the center and another is on the circle.
Property of Central Angles
The angle formed by an arc at the center is twice the inscribed angle formed by the same arc.
Important Formulas: Area and Perimeter
Perimeter:
- • Perimeter or Circumference of a circle = 2 × π × R.
• Length of an Arc = \(\frac{{Central\ Angle\ made\ by\ the\ arc}}{{360^0}}\) × 2 × π × R.
Area:
- • Area of a circle = π × \(R^2\)
• Area of a sector = \(\frac{{Central\ Angle\ made\ by\ the\ arc}}{{360^0}}\)× π × \(R^2\).
Takeaway from this article
Here is a summarized list of all the properties we have learnt in the article.
Want to read more articles like this?
Now, if you liked this article, then I am sure that you want to read some more articles like this.
To read all our article go here: Must Read Articles and Practice Questions to score Q51 !!!!
You will also get a lot of practice questions to learn from.
Happy learning.
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24 Jul 2019, 01:38
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Hey Everyone,
Here is a list of questions specifically designed to help you apply the learnings from this article.
Practice Questions
Question 1
Question 2
Detailed solutions will be posted soon.
Happy Learning!
29 Jul 2019, 04:05
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Hey everyone,
The answers to the practice questions have been posted.
Regards,
e-GMAT
The answers to the practice questions have been posted.
Regards,
e-GMAT
