Selina Textbook Solutions: The Circle | Mathematics Class 6 ICSE PDF Download

 Page 1


IMPORTANT POINTS 
1. A circle is a round enclosed figure, whose mid-point is called its centre. 
 
2. The line segment joining the centre to any point on the circle is called a radius. A 
centre has infinite radii and all radii of a circle are equal. 
3. A line segment which contains the centre of the circle and whose ends points lie on 
the circle is called diameter of the circle. Diameters of a circle are also equal. 
4. Parts of a circle: A circle has three parts (i) Interior (ii) Exterior and (iii) Circle itself. 
 
5. Concentric circles: Two or more circles having the same centre but different radii 
are called concentric circles. 
6. Chord of a circle: A line which divides the circle into two parts is called chord of the 
circle. Diameter is the longest chord of the circle. 
 
7. Segment of a circle: When a chord divides the circle into two unequal parts, the 
bigger part is called the major segment and smaller part is called the minor segment. 
8. Arc of a circle: A part of circumference of a circle is called an arc of the circle. Arc 
greater than half circle is called the major arc and less than half circle is called the minor 
arc. 
9. Sector of a circle: A diameter divides the circle into two equal parts and each part is 
Page 2


IMPORTANT POINTS 
1. A circle is a round enclosed figure, whose mid-point is called its centre. 
 
2. The line segment joining the centre to any point on the circle is called a radius. A 
centre has infinite radii and all radii of a circle are equal. 
3. A line segment which contains the centre of the circle and whose ends points lie on 
the circle is called diameter of the circle. Diameters of a circle are also equal. 
4. Parts of a circle: A circle has three parts (i) Interior (ii) Exterior and (iii) Circle itself. 
 
5. Concentric circles: Two or more circles having the same centre but different radii 
are called concentric circles. 
6. Chord of a circle: A line which divides the circle into two parts is called chord of the 
circle. Diameter is the longest chord of the circle. 
 
7. Segment of a circle: When a chord divides the circle into two unequal parts, the 
bigger part is called the major segment and smaller part is called the minor segment. 
8. Arc of a circle: A part of circumference of a circle is called an arc of the circle. Arc 
greater than half circle is called the major arc and less than half circle is called the minor 
arc. 
9. Sector of a circle: A diameter divides the circle into two equal parts and each part is 
called a semicircle. Sector greater than a semi-circle is called the major sector and less 
than semi-circle is called the minor sector of the circle. 
 
EXERCISE 29 (A) 
Question 1. 
Use the figure given below to fill in the blanks : 
(i) R is the …… of the circle. 
(ii) Diameter of a circle is …… . 
(iii) Tangent to a circle is … . 
(iv) EF is a …… of the circle. 
(v) …… is a chord of the circle. 
(vi) Diameter = 2 x ….. 
(vii) ……. is a radius of the circle. 
(viii) If the length of RS is 5 cm, the length of PQ = …… 
(ix) If PQ is 8 cm long, the length of RS =….. 
(x) AB is a ….. of the circle 
 
Solution: 
(i) center 
(ii) PQ 
(iii)AB 
(iv) secant 
(v) CD 
(vi) radius 
(vii) RS 
(viii) 10 cm 
(ix) 4 cm 
(x) tangent. 
Page 3


IMPORTANT POINTS 
1. A circle is a round enclosed figure, whose mid-point is called its centre. 
 
2. The line segment joining the centre to any point on the circle is called a radius. A 
centre has infinite radii and all radii of a circle are equal. 
3. A line segment which contains the centre of the circle and whose ends points lie on 
the circle is called diameter of the circle. Diameters of a circle are also equal. 
4. Parts of a circle: A circle has three parts (i) Interior (ii) Exterior and (iii) Circle itself. 
 
5. Concentric circles: Two or more circles having the same centre but different radii 
are called concentric circles. 
6. Chord of a circle: A line which divides the circle into two parts is called chord of the 
circle. Diameter is the longest chord of the circle. 
 
7. Segment of a circle: When a chord divides the circle into two unequal parts, the 
bigger part is called the major segment and smaller part is called the minor segment. 
8. Arc of a circle: A part of circumference of a circle is called an arc of the circle. Arc 
greater than half circle is called the major arc and less than half circle is called the minor 
arc. 
9. Sector of a circle: A diameter divides the circle into two equal parts and each part is 
called a semicircle. Sector greater than a semi-circle is called the major sector and less 
than semi-circle is called the minor sector of the circle. 
 
EXERCISE 29 (A) 
Question 1. 
Use the figure given below to fill in the blanks : 
(i) R is the …… of the circle. 
(ii) Diameter of a circle is …… . 
(iii) Tangent to a circle is … . 
(iv) EF is a …… of the circle. 
(v) …… is a chord of the circle. 
(vi) Diameter = 2 x ….. 
(vii) ……. is a radius of the circle. 
(viii) If the length of RS is 5 cm, the length of PQ = …… 
(ix) If PQ is 8 cm long, the length of RS =….. 
(x) AB is a ….. of the circle 
 
Solution: 
(i) center 
(ii) PQ 
(iii)AB 
(iv) secant 
(v) CD 
(vi) radius 
(vii) RS 
(viii) 10 cm 
(ix) 4 cm 
(x) tangent. 
Question 2. 
Draw a circle of radius 4.2 cm. Mark its centre as O. Take a point A on the 
circumference of the circle. Join AO and extend it till it meets point B on the 
circumference of the circle, 
(i) Measure the length of AB. 
(ii) Assign a special name to AB. 
Solution: 
 
(i) By measurement AB = 8.4 cm. 
(ii) ? AB is the diameter of the circle. 
Question 3. 
Draw circle with diameter : 
(i) 6 cm 
(ii) 8.4 cm. 
In each case, measure the length of the radius of the circle drawn. 
Page 4


IMPORTANT POINTS 
1. A circle is a round enclosed figure, whose mid-point is called its centre. 
 
2. The line segment joining the centre to any point on the circle is called a radius. A 
centre has infinite radii and all radii of a circle are equal. 
3. A line segment which contains the centre of the circle and whose ends points lie on 
the circle is called diameter of the circle. Diameters of a circle are also equal. 
4. Parts of a circle: A circle has three parts (i) Interior (ii) Exterior and (iii) Circle itself. 
 
5. Concentric circles: Two or more circles having the same centre but different radii 
are called concentric circles. 
6. Chord of a circle: A line which divides the circle into two parts is called chord of the 
circle. Diameter is the longest chord of the circle. 
 
7. Segment of a circle: When a chord divides the circle into two unequal parts, the 
bigger part is called the major segment and smaller part is called the minor segment. 
8. Arc of a circle: A part of circumference of a circle is called an arc of the circle. Arc 
greater than half circle is called the major arc and less than half circle is called the minor 
arc. 
9. Sector of a circle: A diameter divides the circle into two equal parts and each part is 
called a semicircle. Sector greater than a semi-circle is called the major sector and less 
than semi-circle is called the minor sector of the circle. 
 
EXERCISE 29 (A) 
Question 1. 
Use the figure given below to fill in the blanks : 
(i) R is the …… of the circle. 
(ii) Diameter of a circle is …… . 
(iii) Tangent to a circle is … . 
(iv) EF is a …… of the circle. 
(v) …… is a chord of the circle. 
(vi) Diameter = 2 x ….. 
(vii) ……. is a radius of the circle. 
(viii) If the length of RS is 5 cm, the length of PQ = …… 
(ix) If PQ is 8 cm long, the length of RS =….. 
(x) AB is a ….. of the circle 
 
Solution: 
(i) center 
(ii) PQ 
(iii)AB 
(iv) secant 
(v) CD 
(vi) radius 
(vii) RS 
(viii) 10 cm 
(ix) 4 cm 
(x) tangent. 
Question 2. 
Draw a circle of radius 4.2 cm. Mark its centre as O. Take a point A on the 
circumference of the circle. Join AO and extend it till it meets point B on the 
circumference of the circle, 
(i) Measure the length of AB. 
(ii) Assign a special name to AB. 
Solution: 
 
(i) By measurement AB = 8.4 cm. 
(ii) ? AB is the diameter of the circle. 
Question 3. 
Draw circle with diameter : 
(i) 6 cm 
(ii) 8.4 cm. 
In each case, measure the length of the radius of the circle drawn. 
Solution: 
 
Question 4. 
Draw a circle of radius 6 cm. In the circle, draw a chord AB = 6 cm. 
(i) If O is the centre of the circle, join OA and OB. 
(ii) Assign a special name to ?AOB 
(iii) Write the measure of angle AOB. 
Page 5


IMPORTANT POINTS 
1. A circle is a round enclosed figure, whose mid-point is called its centre. 
 
2. The line segment joining the centre to any point on the circle is called a radius. A 
centre has infinite radii and all radii of a circle are equal. 
3. A line segment which contains the centre of the circle and whose ends points lie on 
the circle is called diameter of the circle. Diameters of a circle are also equal. 
4. Parts of a circle: A circle has three parts (i) Interior (ii) Exterior and (iii) Circle itself. 
 
5. Concentric circles: Two or more circles having the same centre but different radii 
are called concentric circles. 
6. Chord of a circle: A line which divides the circle into two parts is called chord of the 
circle. Diameter is the longest chord of the circle. 
 
7. Segment of a circle: When a chord divides the circle into two unequal parts, the 
bigger part is called the major segment and smaller part is called the minor segment. 
8. Arc of a circle: A part of circumference of a circle is called an arc of the circle. Arc 
greater than half circle is called the major arc and less than half circle is called the minor 
arc. 
9. Sector of a circle: A diameter divides the circle into two equal parts and each part is 
called a semicircle. Sector greater than a semi-circle is called the major sector and less 
than semi-circle is called the minor sector of the circle. 
 
EXERCISE 29 (A) 
Question 1. 
Use the figure given below to fill in the blanks : 
(i) R is the …… of the circle. 
(ii) Diameter of a circle is …… . 
(iii) Tangent to a circle is … . 
(iv) EF is a …… of the circle. 
(v) …… is a chord of the circle. 
(vi) Diameter = 2 x ….. 
(vii) ……. is a radius of the circle. 
(viii) If the length of RS is 5 cm, the length of PQ = …… 
(ix) If PQ is 8 cm long, the length of RS =….. 
(x) AB is a ….. of the circle 
 
Solution: 
(i) center 
(ii) PQ 
(iii)AB 
(iv) secant 
(v) CD 
(vi) radius 
(vii) RS 
(viii) 10 cm 
(ix) 4 cm 
(x) tangent. 
Question 2. 
Draw a circle of radius 4.2 cm. Mark its centre as O. Take a point A on the 
circumference of the circle. Join AO and extend it till it meets point B on the 
circumference of the circle, 
(i) Measure the length of AB. 
(ii) Assign a special name to AB. 
Solution: 
 
(i) By measurement AB = 8.4 cm. 
(ii) ? AB is the diameter of the circle. 
Question 3. 
Draw circle with diameter : 
(i) 6 cm 
(ii) 8.4 cm. 
In each case, measure the length of the radius of the circle drawn. 
Solution: 
 
Question 4. 
Draw a circle of radius 6 cm. In the circle, draw a chord AB = 6 cm. 
(i) If O is the centre of the circle, join OA and OB. 
(ii) Assign a special name to ?AOB 
(iii) Write the measure of angle AOB. 
Solution: 
 
Question 5. 
Draw a circle of radius 4.8 cm and mark its centre as P. 
(i) Draw radii PA and PB such that ?APB = 45°. 
(ii) Shade the major sector of the circle 
Solution: 
 
PA is the radius of circle. i.c., PA = 4.8 cm. 
(i) ?APB = 45° in which P is the centre of the circle and PA and PB are radii of circle. 
(ii) Major sector of circle is shaded in the figure. 
Question 6. 
Draw a circle of radius 3.6 cm. In the circle, draw a chord AB = 5 cm. Now shade 
the minor segment of the circle. 
Solution: