Selina Textbook Solutions: Circle: Tangents and Intersecting Chords | Mathematics Class 10 ICSE PDF Download

 Page 1


Tangents and Intersecting Chords 
 
Exercise 18A 
Question 1. 
The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from 
a point at a distance of 10 cm from its centre? 
 
Solution: 
 
 
Question 2. 
In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If 
AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle. 
Page 2


Tangents and Intersecting Chords 
 
Exercise 18A 
Question 1. 
The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from 
a point at a distance of 10 cm from its centre? 
 
Solution: 
 
 
Question 2. 
In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If 
AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle. 
 
 
Solution: 
 
Question 3. 
Two circles touch each other externally at point P. Q is a point on the common tangent 
through P. Prove that the tangents QA and QB are equal. 
 
 
Page 3


Tangents and Intersecting Chords 
 
Exercise 18A 
Question 1. 
The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from 
a point at a distance of 10 cm from its centre? 
 
Solution: 
 
 
Question 2. 
In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If 
AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle. 
 
 
Solution: 
 
Question 3. 
Two circles touch each other externally at point P. Q is a point on the common tangent 
through P. Prove that the tangents QA and QB are equal. 
 
 
Solution: 
 
 
Question 4. 
Two circles touch each other internally. Show that the tangents drawn to the two circles 
from any point on the common tangent are equal in length. 
 
Solution: 
 
 
Question 5. 
Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the 
outer circle which touches the inner. 
 
Page 4


Tangents and Intersecting Chords 
 
Exercise 18A 
Question 1. 
The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from 
a point at a distance of 10 cm from its centre? 
 
Solution: 
 
 
Question 2. 
In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If 
AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle. 
 
 
Solution: 
 
Question 3. 
Two circles touch each other externally at point P. Q is a point on the common tangent 
through P. Prove that the tangents QA and QB are equal. 
 
 
Solution: 
 
 
Question 4. 
Two circles touch each other internally. Show that the tangents drawn to the two circles 
from any point on the common tangent are equal in length. 
 
Solution: 
 
 
Question 5. 
Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the 
outer circle which touches the inner. 
 
Solution: 
 
 
Question 6. 
 
Three circles touch each other externally. A triangle is formed when the centers of these 
circles are joined together. Find the radii of the circles, if the sides of the triangle formed 
are 6 cm, 8 cm and 9 cm. 
 
Solution: 
Page 5


Tangents and Intersecting Chords 
 
Exercise 18A 
Question 1. 
The radius of a circle is 8 cm. Calculate the length of a tangent drawn to this circle from 
a point at a distance of 10 cm from its centre? 
 
Solution: 
 
 
Question 2. 
In the given figure, O is the centre of the circle and AB is a tangent to the circle at B. If 
AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle. 
 
 
Solution: 
 
Question 3. 
Two circles touch each other externally at point P. Q is a point on the common tangent 
through P. Prove that the tangents QA and QB are equal. 
 
 
Solution: 
 
 
Question 4. 
Two circles touch each other internally. Show that the tangents drawn to the two circles 
from any point on the common tangent are equal in length. 
 
Solution: 
 
 
Question 5. 
Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the 
outer circle which touches the inner. 
 
Solution: 
 
 
Question 6. 
 
Three circles touch each other externally. A triangle is formed when the centers of these 
circles are joined together. Find the radii of the circles, if the sides of the triangle formed 
are 6 cm, 8 cm and 9 cm. 
 
Solution: 
 
Question 7. 
If the sides of a quadrilateral ABCD touch a circle, prove that AB + CD = BC + AD.