ML Aggarwal: Circle - Class 8 PDF Download

 Page 1


 
1. Draw a circle with centre O and radius 2.5 cm. Draw two radii OA 
and OB such that ?AOB = 60
0
. Measure the length of the chord AB. 
Solution: 
1. Draw a circle, taking centre as O and radius equal to 2.5 cm 
2. Join OA, where A is any point on the circle 
3. Draw ?AOB equal to 60
0
 
4. Now, join AB and on measuring we get, AB = 2.5 cm 
 
 
2. Draw a circle of radius 3.2 cm. Draw a chord AB of this circle such 
that AB = 5 cm. Shade the minor segment of the circle. 
Solution: 
1. Draw a circle, taking centre as O and radius = 3.2 cm 
2. Take a point A on the circle 
3. Taking A as centre and radius = 5 cm, draw an arc to meet the circle at 
point B 
Page 2


 
1. Draw a circle with centre O and radius 2.5 cm. Draw two radii OA 
and OB such that ?AOB = 60
0
. Measure the length of the chord AB. 
Solution: 
1. Draw a circle, taking centre as O and radius equal to 2.5 cm 
2. Join OA, where A is any point on the circle 
3. Draw ?AOB equal to 60
0
 
4. Now, join AB and on measuring we get, AB = 2.5 cm 
 
 
2. Draw a circle of radius 3.2 cm. Draw a chord AB of this circle such 
that AB = 5 cm. Shade the minor segment of the circle. 
Solution: 
1. Draw a circle, taking centre as O and radius = 3.2 cm 
2. Take a point A on the circle 
3. Taking A as centre and radius = 5 cm, draw an arc to meet the circle at 
point B 
4. Now, join AB and shade the minor segment of the circle 
 
 
3. Find the length of the tangent drawn to a circle of radius 3 cm, from 
a point at a distance 5 cm from the centre. 
Solution: 
Draw a circle, taking C as centre and radius CT = 3 cm 
Let PT be the tangent, drawn from point P to a circle with centre C 
Let CP = 5 cm 
CT = 3 cm (given) 
 
?CTP = 90
0
 (since radius is perpendicular to tangent) 
Page 3


 
1. Draw a circle with centre O and radius 2.5 cm. Draw two radii OA 
and OB such that ?AOB = 60
0
. Measure the length of the chord AB. 
Solution: 
1. Draw a circle, taking centre as O and radius equal to 2.5 cm 
2. Join OA, where A is any point on the circle 
3. Draw ?AOB equal to 60
0
 
4. Now, join AB and on measuring we get, AB = 2.5 cm 
 
 
2. Draw a circle of radius 3.2 cm. Draw a chord AB of this circle such 
that AB = 5 cm. Shade the minor segment of the circle. 
Solution: 
1. Draw a circle, taking centre as O and radius = 3.2 cm 
2. Take a point A on the circle 
3. Taking A as centre and radius = 5 cm, draw an arc to meet the circle at 
point B 
4. Now, join AB and shade the minor segment of the circle 
 
 
3. Find the length of the tangent drawn to a circle of radius 3 cm, from 
a point at a distance 5 cm from the centre. 
Solution: 
Draw a circle, taking C as centre and radius CT = 3 cm 
Let PT be the tangent, drawn from point P to a circle with centre C 
Let CP = 5 cm 
CT = 3 cm (given) 
 
?CTP = 90
0
 (since radius is perpendicular to tangent) 
From ?CPT, 
CP
2
 = PT
2
 + CT
2
 (By Pythagoras theorem) 
(5)
2
 = PT
2
 + (3)
2
 
We get, 
PT
2
 = 25 – 9 
PT
2
 = 16 
PT = v16 
We get, 
PT = 4 
Therefore, length of tangent = 4 cm 
 
4. In the adjoining figure, PT is a tangent to the circle with centre C. 
Given CP = 20 cm and PT = 16 cm, find the radius of the circle. 
 
Solution: 
We know that, 
Radius is always perpendicular to tangent 
i.e., CT ? PT 
Therefore, 
Page 4


 
1. Draw a circle with centre O and radius 2.5 cm. Draw two radii OA 
and OB such that ?AOB = 60
0
. Measure the length of the chord AB. 
Solution: 
1. Draw a circle, taking centre as O and radius equal to 2.5 cm 
2. Join OA, where A is any point on the circle 
3. Draw ?AOB equal to 60
0
 
4. Now, join AB and on measuring we get, AB = 2.5 cm 
 
 
2. Draw a circle of radius 3.2 cm. Draw a chord AB of this circle such 
that AB = 5 cm. Shade the minor segment of the circle. 
Solution: 
1. Draw a circle, taking centre as O and radius = 3.2 cm 
2. Take a point A on the circle 
3. Taking A as centre and radius = 5 cm, draw an arc to meet the circle at 
point B 
4. Now, join AB and shade the minor segment of the circle 
 
 
3. Find the length of the tangent drawn to a circle of radius 3 cm, from 
a point at a distance 5 cm from the centre. 
Solution: 
Draw a circle, taking C as centre and radius CT = 3 cm 
Let PT be the tangent, drawn from point P to a circle with centre C 
Let CP = 5 cm 
CT = 3 cm (given) 
 
?CTP = 90
0
 (since radius is perpendicular to tangent) 
From ?CPT, 
CP
2
 = PT
2
 + CT
2
 (By Pythagoras theorem) 
(5)
2
 = PT
2
 + (3)
2
 
We get, 
PT
2
 = 25 – 9 
PT
2
 = 16 
PT = v16 
We get, 
PT = 4 
Therefore, length of tangent = 4 cm 
 
4. In the adjoining figure, PT is a tangent to the circle with centre C. 
Given CP = 20 cm and PT = 16 cm, find the radius of the circle. 
 
Solution: 
We know that, 
Radius is always perpendicular to tangent 
i.e., CT ? PT 
Therefore, 
?CPT is a right angled triangle, where CP = hypotenuse 
In right angled triangle, 
By Pythagoras theorem, we get, 
CP
2
 = PT
2
 + CT
2
 
CT
2
 = CP
2
 – PT
2
 
CT
2
 = (20)
2
 – (16)
2
 
We get, 
CT
2
 = 400 – 256 
CT
2
 = 144 
CT = v144 
We get, 
CT = 12 cm 
Therefore, radius of circle = 12 cm 
 
5. In each of the following figure, O is the centre of the circle. Find 
the size of each lettered angle: 
Page 5


 
1. Draw a circle with centre O and radius 2.5 cm. Draw two radii OA 
and OB such that ?AOB = 60
0
. Measure the length of the chord AB. 
Solution: 
1. Draw a circle, taking centre as O and radius equal to 2.5 cm 
2. Join OA, where A is any point on the circle 
3. Draw ?AOB equal to 60
0
 
4. Now, join AB and on measuring we get, AB = 2.5 cm 
 
 
2. Draw a circle of radius 3.2 cm. Draw a chord AB of this circle such 
that AB = 5 cm. Shade the minor segment of the circle. 
Solution: 
1. Draw a circle, taking centre as O and radius = 3.2 cm 
2. Take a point A on the circle 
3. Taking A as centre and radius = 5 cm, draw an arc to meet the circle at 
point B 
4. Now, join AB and shade the minor segment of the circle 
 
 
3. Find the length of the tangent drawn to a circle of radius 3 cm, from 
a point at a distance 5 cm from the centre. 
Solution: 
Draw a circle, taking C as centre and radius CT = 3 cm 
Let PT be the tangent, drawn from point P to a circle with centre C 
Let CP = 5 cm 
CT = 3 cm (given) 
 
?CTP = 90
0
 (since radius is perpendicular to tangent) 
From ?CPT, 
CP
2
 = PT
2
 + CT
2
 (By Pythagoras theorem) 
(5)
2
 = PT
2
 + (3)
2
 
We get, 
PT
2
 = 25 – 9 
PT
2
 = 16 
PT = v16 
We get, 
PT = 4 
Therefore, length of tangent = 4 cm 
 
4. In the adjoining figure, PT is a tangent to the circle with centre C. 
Given CP = 20 cm and PT = 16 cm, find the radius of the circle. 
 
Solution: 
We know that, 
Radius is always perpendicular to tangent 
i.e., CT ? PT 
Therefore, 
?CPT is a right angled triangle, where CP = hypotenuse 
In right angled triangle, 
By Pythagoras theorem, we get, 
CP
2
 = PT
2
 + CT
2
 
CT
2
 = CP
2
 – PT
2
 
CT
2
 = (20)
2
 – (16)
2
 
We get, 
CT
2
 = 400 – 256 
CT
2
 = 144 
CT = v144 
We get, 
CT = 12 cm 
Therefore, radius of circle = 12 cm 
 
5. In each of the following figure, O is the centre of the circle. Find 
the size of each lettered angle: 
 
Solution: 
(i) In the given figure, 
AB is the diameter and O is the centre of the circle 
Given ?CAB = 32
0
 
?ABD = 50
0
 
?C = 90
0
 (angles in the semicircle) 
By angle sum property of triangle, we get, 
?C + ?CAB + ?ABC = 180
0
 
90
0
 + ?CAB + ?x = 180
0
 
90
0
 + 32
0
 + ?x = 180
0
 
32
0
 + ?x = 180
0
 – 90
0