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In our daily life, we see many things which have a circular shape. For example, one-rupee, two-rupees and five-rupees coins, bangles and wheels, etc. They form a circle.
A circle is the set of all those point in a plane whose distance from a fixed point remains constant.
The fixed point is called the centre of the circle and the constant distance is known as the radius of the circle.
Full moon is the example of a circle.
A Circle has an interior as well as an exterior region as shown in the below figure.
Here the points A, B and M lie in the exterior of the circle.
The points D, P and X lies in the interior of the circle.
The point R, Q, N lie on the circle.
The centre O of the circle always lies in the interior of the circle.
Consider a circle with centre O and radius r.
(i) The part of the plane consisting of the point A, for which OA < r, is called the interior of the circle.
(ii) The part of the plane consisting of the point B, for which OB = r, is the circle itself.
(iii) The part of the plane consisting of the point C, for which OC > r, is called the exterior of the circle.
Solution:
The point P at which we place the needle end of the compass and move the pencil around is the center of the circle.
The centre of a circle lies in its interior.
Solution:
The length of the boundary of the circle is its circumference.
In other words, it is the perimeter of the circle.
Solution:
The line segment joining the centre to any point on the circle is called the radius of the circle.
Take any point N on the circle and joint it with the centre M. The line segment MN is the radius of the circle.
Note:
MN = MO = MP → (Radii)
All the radii of a circle are equal in length. We can draw as many radii as we want. MN = MO = MP → (Radii)
All the radii of a circle are equal in length. We can draw as many radii as we want.
Solution:
Let us produce the radius PQ to meet another point O on the circle. We get a line segment OQ with its end points O & Q on the circle. It passes through the centre P.
Such a line segment is called a diameter.
The length of a diameter of a circle is twice the length of the radius of the circle.
OP = 3.5 cm
PQ = 3.5 cm
OQ = 3.5 cm + 3.5 cm
Therefore, OQ = 7.0 cm
Solution:
The line segment joining any two points on the circle is the chord of the circle. The end points A and B of line segment AB lie on the circle.
So, AB is the chord of the circle.
Chords of a circle may or may not be equal in length. Diameter of a circle is the longest chord.
Solution:
Any part of a circle is called an arc of the circle. An arc is usually named by 3 points.
ACB is an arc of the given circle.
Solution:
The end points of a diameter of a circle divide the circle into two parts; each part is called a semi-circular region.
AXB and AYB are two semi circles.
Two or more circles with the same centre are called concentric circles.
In the above figure, three concentric circles with same centre O are drawn.
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1. What is the Definition of Circle in Maths?
Answer:
A circle is a closed plane curve figure whose each point is at a equal distance from a fixed point called the centre of the circle.
For Example: O is the centre of circle in the given figure below. A circle is represented by O.
Answer:
A line segment joining the centre to any point on the circle is called the radius.
For Example: OA is the radius of the circle. OA, OB and OC are the radii of the circle in the figure below OA = OB = OC. (Radii is the plural of radius)
Answer:
A chord is a line segment whose end points lie on a circle A chord may or may not pass through the centre of the circle.
In the figure below, AB, CD, MN and PQ are the chords of the circle.
Answer:
If the chord of a circle passes through the centre, it is called the diameter of the circle.
We can also say, Diameter is a line segment whose two end points lie on the circle and it passes through the centre in the figure below, AB and PQ are the diameters of the circle which pass through its centre O. A diameter is the longest chord of a circle
Remember:
Diameter = 2 x Radius of the Circle
Answer:
The diameter of a circle divides the circle in two equal parts. Each half of the circle is called a semi-circle.
Answer:
The length of the circle is called its circumference. We cannot measure the length of a circle with the help of a scale. We measure it with the help of a thread. We first wrap the thread round the circle and then measure the length of the thread which is the circumference of the given circle.
Answer:
A part of the circumference is called the arc of a circle.
Here in the figure below, ABC is an arc.
Answer:
A circle divides the plane into three parts.
(i) Interior of the circle
(ii) Exterior of the circle
(iii) Circle itself
In the given figure below, point A lies in the interior of the circle. Point C lies in the exterior of the circle, and point B lies on the circle.
All the above are the Parts of a Circle or Terms Related to the Circle.
● Circle
Relation between Diameter Radius and Circumference.
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