Properties Of Circle: If you are looking for Properties of Circle, you have come to the right place. Circle is an important geometrical shape that we see in abundance in our day-to-day life. From the doughnut that we eat to wheels/tires of vehicles to the moon in the night sky, there is no dearth of objects that are circular in shape. Students are introduced to the various concepts related to circles in elementary or primary classes. More complex topics are taught in higher classes.
Circle is important not only for school-level and board exams but also for various other exams, like CAT, MAT, and exams for government job recruitment. So, in this article, we will discuss the properties of circles. Read on to find out.
Properties Of Circle
The word ‘circle’ is derived from the Greek word ‘kirkos‘, which means hoop or ring. Before getting into the properties of circles, let’s have a look at the definition of circle and some common terminologies related to it.
Circle Definition: What Is A Circle?
A circle is a round and closed plane figure. The boundary of a circle, also called the circumference of the circle, consists of points that are all equidistant from another point inside the circle, called the center. The line joining the center and any point on the circumference of the circle is called the radius of the circle.
Common Terminologies Related To Circle
Let us now look into some common terminologies related to circle:
Center: It is the point inside the circle from which all the points on the boundary of the circle are equally located. It is usually denoted by ‘O’.
Circumference: It is the boundary of the circle. All points on the circumference of the circle are at equal distance from the center of the circle.
Radius: It is the straight line joining the center of the circle and any point on the circumference. The radius of a circle is usually denoted by ‘r’.
Diameter: The diameter of a circle, denoted by ‘D’, is the line that passes through the center of the circle and joins two points on its circumference. The diameter is twice the length of the radius, i.e. D = 2r.
Arc: Any segment of the circumference of a circle is called an arc. In the above diagram, the yellow segment of the circumference is an arc.
We can create two arcs if two points are given on the circumference of a circle. The longer arc is called the Major Arc while the shorter one is called Minor Arc.
Sector: Any pie-shaped part of a circle that is enclosed inside two radii of the circle and their intercepted arc is called a sector. In the above diagram, the pink part of the circle is a sector.
Chord: A line segment joining any two points on the circumference of a circle is called a chord.
Secant: A line that cuts two points on the circumference of a circle is called a secant or secant line. It is, basically, a chord that extends beyond the circumference of a circle.
Tangent: A line that touches the circumference of a circle at one single point is called a tangent of the circle.
Properties Of Circle
Let us now look into some of the most important properties of circle:
- a. Circles having equal radii are said to be congruent.
- b. The diameter of a circle is the longest chord of the circle.
- c. The perpendicular drawn on any given chord of a circle from the center of the circle bisects the chord into two equal halves.
- d. All chords of a circle equidistant from the center of the circle are equal in length.
- e. If we draw two tangents to a circle from a given point outside the circle, then the two tangents will be equal in length.
- f. A tangent to a circle and the radius of the circle at the point of contact of the tangent form a right angle.
- g. The angle subtended at the center of a circle by the circumference of the circle is equal to 360°.
- h. The circumference of a circle is proportional to its radius.
- i. You can draw a triangle, square, trapezium, rectangle, or kite inside a circle with all their vertices exactly on the circumference of the circle.
- j. The length of a chord of a circle is inversely proportional to the perpendicular distance of it from the center of the circle.
- k. You can inscribe a circle inside a triangle, square, or kite.
- l. Two tangents drawn to a circle at the two endpoints of a diameter are parallel to each other.
Equation Of A Circle
The equation of a circle with its center at (h, k) is given by:
(x – h)2 + (y – k)2 = r2
where r = radius of the circle.
Some of the basic formulas related to circle are as under:
|Diameter of a Circle, D||2r|
|Area of a Circle, A||πr2|
|Circumference of a Circle||2πr|
|Area of a Semi-circle||πr2/2|
|Perimeter of a Semi-circle||πr + 2r = πr + D|
Problems On Circle
Here are a few example problems on Circle:
Example 1: Find the area of a circle whose diameter is 28 cm.
Here, Diameter, D = 28 cm.
Therefore, radius, r = 28/2 cm = 14 cm.
Area of a circle = πr2 = (22/7) X 142 = 616 cm2.
Example 2: Find the circumference of a semicircle whose radius is 7 cm.
Circumference of a Semi-circle = πr + 2r = [(22/7) X 7] + (2 X 7) = 22 + 14 = 36 cm.
So, now you know the properties of circle. Solve more circle practice questions and master the concepts.
Other Articles On Maths
Some other helpful articles by Embibe are provided below:
|HCF And LCM|
|Properties Of Triangles|
Basic mathematical and computational ability is important for everyone and not just students who want to opt Science in their Higher Secondary education. It is important for school-level Maths exams, the board exams, and also for various competitive exams like CAT, MAT, and exams for government job recruitment. It is, therefore, important for students to take the subject seriously from the early classes.
At Embibe, we provide free Maths practice questions for Class 8, 9, 10, 11, and 12 along with detailed solutions:
|a. Class 8 Maths Practice Questions|
|b. Class 9 Maths Practice Questions|
|c. Class 10 Maths Practice Questions|
|d. Class 11-12 Maths Practice Questions|
So, make the best use of these resources and master the subject.
We hope this article on Properties of Circle helps you. If you have any queries, feel free to ask in the comment section below. We will get back to you at the earliest.526 Views