WBBSE Notes For Class 6 Maths Geometry Chapter 4 Geometrical Concept Of Circle

Geometry Chapter 4 Geometrical Concept Of Circle

Geometry Chapter 4 What Is Circle

Definition:

Circle

1. A circle is a plane surface enclosed by a single curved line in such a way that every point on this curved line is equidistant from a fixed point inside it in the same plane.
2. This definition can also be written in the following way:
3. In a plane surface if a point moves in such a way that its distance from a fixed point in the same plane is always equal to a given distance, then the locus of
4. the movable point is called a circle.
   
5. The fixed point is called the centre of the circle and the given distance is called the radius of the circle
6. In the above O is a fixed point, and point A (the point lies in the same plane as that O) is moving around in such a way that in any position of A, the distance of A from O is always equal to a given distance i.e., the distance of A from O is always constant. Here the distances OA, OB, OC, and OD are always the same.
7. The locus of point A i.e., ABCDA is a circle
8. O is the centre of the circle

 

WBBSE Class 6 Circle Notes

Geometry Chapter 4 Different Parts Of A Circle

 

Important Definitions Related to Circles

Centre of the circle :

1. The fixed point which lies inside the circle around which the movable point moves is called the centre of the circle.
2. In the above, O is the centre of the circle.

Circumference of the circle:

1. The locus of the movable point i.e., the curved line is called the circumference of the circle.
2. In the above ANMBQPA, the curved line in which the movable point A moves is the circumference of the circle.

The radius of the circle:

1. The length of the line segment obtained by joining the centre to any point on
2. the circumference of the circle is called the radius of the circle.
3. Or, The constant distance from the centre of the circle to any point on the circumference of the circle is called the radius of the circle.
4. In the above figure, O is the centre of the circle. Each of the lengths \(\overline{\mathrm{OA}}\),
   \(\overline{\mathrm{ON}}\), \(\overline{\mathrm{OM}}\), \(\overline{\mathrm{OB}}\), \(\overline{\mathrm{OQ}}\) and \(\overline{\mathrm{PQ}}\)
5. is the radius of the circle.
6. It is clear that \(\overline{\mathrm{OA}}\) = \(\overline{\mathrm{ON}}\) = \(\overline{\mathrm{OM}}\) = \(\overline{\mathrm{OB}}\) = \(\overline{\mathrm{OQ}}\) = \(\overline{\mathrm{OP}}\) = r, where r is the radius of the circle.

Understanding Circles

Diameter of the circle :

1. The line segment which passes through the centre of the circle and is bounded by the circumference is called the diameter of the circle.
2. In the above AB is the diameter of the circle and it is generally denoted by the symbol “d”.
3. The line segment is obtained by joining two points on the circumference of the circle and passing through the centre of the circle.
4. In any circle, the diameter is twice the radius.
5. ∴ d = 2r or, diameter = 2 x radius.

Chord of a circle :

1. The line segment obtained by joining any two points on the circumference of the circle is called a chord of the circle.
2. In the above, both PQ and AB are the chords of the circle centred at O.

Arc of a circle :

1. Any part of the circumference of a circle is called an Arc of the circle.
2. In the above figure, BMN is an arc. It is denoted by arc \(\overparen{B M N}\)
3. Any chord of a circle other than the diameter divides the circumference of the circle into two arcs.
4. So the arcs of a circle are of two types:
   1. Minor Arc and
   2. Major Arc.

1. Minor Arc:

1. The smaller arc is called the Minor Arc.
2. In the figure alongside PR is a chord and it divides the circumference into two arcs; PQR\(\overparen{P Q R}\) and arc \(\overparen{P M R}\).
3. Here PQR\(\) is smaller than the arc \(\overparen{P M R}\).
4. So arc PQR is a Minor Arc.

 

 

2. Major Arc:

1. The larger arc is called the Major Arc.
2. In the figure,\(\overparen{P M R}\) is the Major arc, because it is larger than the arc \(\overparen{P Q R}\)

 

 

The sector of a circle:

1. The part of the circle bounded by an arc and the two radii is called a sector of the circle.
2. The OAB is a sector of the circle.
3. In (1) below, there are eight sectors of the circle.
4. In (2) there are six sectors of the circle.

 

 

Semi-circle:

1. The half part of a circle is called Semi-circle.
2. A diameter of a circle divides it into two equal parts, each part is called a semi-circle.
3. In the above, ACB is a semi-circle.
4. The centre of the circle is the centre of the semi-circle and the radius of the circle is the radius of the semi-circle.

Concentric circles:

1. Circles which have the same centre are called concentric circles.
2. Concentric circles have the same centre but their radii are different.

Geometry Chapter 4 Some Properties Of Circle

1. The diameter of a circle is the largest chord of the circle.
2. All chords of equal length of a circle are equidistant from the centre of the circle.
3. All equidistant chords from the centre of a circle are equal in length.
4. The angle in a semi-circle is a right angle.
5. Equal arcs of a circle subtend equal angles at the centre of the circle.
6. The circumference of a circle = 2nr, r= radius
   (\(\pi=\frac{22}{7}\), the symbol π is read as pie).
7. A straight line drawn from the centre of a circle to bisect a chord, which is not a diameter, is at right angles to the chord.
8. The perpendicular to a chord from the centre bisects the chord.