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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