Circle Theorem Class-9th Concise Selina ICSE Mathematics Solutions Chapter-17 by RK Bansal .  We provide step by step Solutions of Exercise / lesson-17 Circle Theorem for ICSE Class-9 Concise Selina Mathematics by R K Bansal.

Our Solutions contain all type Questions with Exe-17 A , Exe-17 B, Exe-17 C and Exe-17 D, to develop skill and confidence. Visit official Website for detail information about ICSE Board Class-9 Mathematics .

## Circle Theorem Class-9th Concise Selina ICSE Mathematics Solutions Chapter-17

–: Select Topics :–

Exe-17 A,

Exe-17 B,

Exe-17 C,

Exe-17 D,

### Exercise-17 A,Circle Theorem Class-9th Concise Selina ICSE Mathematics Solutions

#### Question 1

A chord of length 6 cm is drawn in a circle of radius 5 cm. Calculate its distance from the center of the circle.

Let AB be the chord and O be the centre of the circle.

Let OC be the perpendicular drawn from O to AB. We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.

AC = CB = 3 cm #### Question 2

A chord of length 8 cm is drawn at a distance of 3 cm from the centre of the circle. Calculate the radius of the circle.

Let AB be the chord and O be the centre of the circle.

Let OC be the perpendicular drawn from O to AB. Hence, radius of the circle is 5 cm.

#### Question 4

A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the centre.

Let AB be the chord of length 24 cm and O be the centre of the circle.

Let OC be the perpendicular drawn from O to AB.

We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.

AC = CB = 12 cm #### Question 5

In the following figure, AD is a straight line,…….. and O is the centre of both the circles. If OA = 34cm, OB = 20 cm and OP = 16 cm; find the length of AB.

………………

#### We know that the perpendicular to a chord, from the centre of a circle, bisects the chord.

AP = PD

By Pythagoras Theorem,

OA2 = OP2 + AP2

=> AP2 = (34)2 – (16)= 900

=> AP = 30 cm

AB = AP – BP = 30 – 12 = 18 cm

#### Question 6

In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Find the distance between the chords, if both the chords are:

(i) on the opposite sides of the centre;

(ii) on the same side of the centre.

Let O be the centre of the circle and AB and CD be the two parallel chords of length 30 cm and 16 cm respectively.

Drop OE and OF perpendicular on AB and CD from the centre O. #### Question 7

Two parallel chords are drawn in a circle of diameter 30.0 cm. The length of one chord is 24.0 cm and the distance between the two chords is 21.0 cm; find the length of another chord.

Since the distance between the chords is greater than the radius of the circle (15 cm), so the chords will be on the opposite sides of the centre. Question 8

A chord CD of a circle whose centre is O, is bisected at P by a diameter AB. Given OA = OB = 15 cm and OP = 9 cm. Calculate the lengths of:

(i) CD ; (ii) AD ; (iii) CB.

#### Question 9

The figure given below shows a circle with centre O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm, find the radius of the circle.

…………..

#### Question 10

In the given figure, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm, Find the :

(ii) length of chord CD ### Exercise-17 B Circle Theorem Class-9th Concise Selina ICSE Mathematics Solutions

#### Question 1

The figure shows two concentric circles and AD is a chord of larger circle. Prove that: AB = CD.

……………….

#### Question 2

A straight line is drawn cutting two equal circles and passing through the mid-point M of the line joining their centres O and O’. Prove that the chords AB and CD, which are intercepted by the two circles, are equal.

………………. #### Question 3

M and N are the mid-points of two equal chords AB and CD respectively of a circle with centre O. Prove that:

(i)………………..

(ii)…………..

#### Question 4

In the following figure; P and Q are the points of intersection of two circles with centres O and O’. If straight lines APB and CQD are parallel to OO’; prove that:

(i)………………..

(ii)…………..

Drop OM and O’N perpendicular on AB and OM’ and O’N’ perpendicular on CD. #### Question 5

Two equal chords AB and CD of a circle with centre O, intersect each other at point P inside the circle. Prove that:

(i) AP = CP ; (ii) BP = DP

………..

Drop OM and ON perpendicular on AB and CD.

Join OP, OB and OD. #### Question 6

In the following figure, OABC is a square. A circle is drawn with O as centre which meets OC at P and OA at Q. Prove that:

(i)………………..

(ii)…………..

#### Question 7

The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles be 50 cm and 34 cm, calculate the distance between their centres.

#### Question 8

The line joining the midpoints of two chords of a circle passes through its centre. Prove that the chords are parallel.

#### Question 9

In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centres of the circles. Show that:

(i) AB = CD ;

(ii) AC = BD.

………….

#### Question 10

AB and CD are two equal chords of a circle with centre O which intersect each other at right angle at point P. If OM  AB and ONCD; show that OMPN is a square. ### Exercise-17 C, Circle theorem Class-9th Concise Selina ICSE Mathematics Solutions

#### Question 1

In the given figure, an equilateral triangle ABC is inscribed in a circle with centre O.

Find: (i) ∠BOC (ii) ∠OBC

……………

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