## Chapter 17 - Circles Exercise Ex. 17.1

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3

Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Find the diameter of the circle if the length of a chord is 3.2cm and its distance from the centre is 1.2cm.
Solution 12
Question 13

Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
A chord of length 16.8cm is at a distance of 11.2cm from the centre of a circle. Find the length of the chord of the same circle which is at a distance of 8.4cm from the centre.
Solution 16
Question 17
A chord of length 6cm is at a distance of 7.2cm from the centre of a circle. Another chord of the same circle is of length 14.4cm. Find its distance from the centre.
Solution 17
Question 18
A chord of length 8cm is drawn inside a circle of radius 6cm. Find the perpendicular distance of the chord from the centre of the circle.
Solution 18
Question 19
Two circles of radii 5cm and 3cm with centres O and P touch each other internally. If the perpendicular bisector of the line segment OP meets the circumference of the larger circle at A and B, find the length of AB.
Solution 19
Question 20
Two chords AB and CD of lengths 6cm and 12cm are drawn parallel inside the circle. If the distance between the chords of the circle is 3cm, find the radius of the circle.
Solution 20
Question 21
Two chords of lengths 10cm and 24cm are drawn parallel o each other in a circle. If they are on the same side of the centre and the distance between them is 17cm, find the radius of the circle.
Solution 21
Question 22

Solution 22

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24

## Chapter 17 - Circles Exercise Ex. 17.3

Question 1
Find the length of the tangent from a point which is at a distance of 5cm from the centre of the circle of radius 3cm.
Solution 1
Question 2
Solution 2
Question 3
In fig., chords AB and CD of a circle intersect at P. AP = 5cm, BP= 3cm and CP = 2.5cm. Determine the length of DP.
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
The length of the direct common tangent to two circles of radii 12cm and 4cm is 15cm. calculate the distance between their centres.
Solution 10
Question 11
Solution 11
Question 12
A point A is 17cm from the centre of the circle. The length of the tangent drawn from A to the circle is 15cm. find the radius of the circle.
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
PA and PB are tangents from P to the circle with centre O. At M, a tangent is drawn cutting PA at K and PB at N. Prove that KN = AK + BN.
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
Solution 21
Question 22
Solution 22