Exercise 17(A) Page:210 - Byju's

[Pages:37]Concise Selina Solutions for Class 9 Maths Chapter 17Circles

Exercise 17(A)

Page:210

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

Solution: 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

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

Solution: 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.

Concise Selina Solutions for Class 9 Maths Chapter 17Circles

Hence, radius of the circle is 5 cm. 3. The radius of a circle is 17.0 cm and the length of perpendicular is drawn from its center to a chord

is 8-0 cm. Calculate the length if the chord. Solution:

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

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.

Solution: 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

Concise Selina Solutions for Class 9 Maths Chapter 17Circles

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

Solution:

For the inner circle, BC is a chord and

.

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

BP = PC

For the outer circle, AD is the chord and

.

Concise Selina Solutions for Class 9 Maths Chapter 17Circles

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)2 = 900 => AP = 30 cm AB = AP - BP = 30 - 12 = 18 cm

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 chords are: (i) On the opposite sides of the centre, (ii) On the same side of the centre.

Solution: 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.

Concise Selina Solutions for Class 9 Maths Chapter 17Circles

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 c; find the length of the outer chord.

Solution: 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.

Let O be the centre of the circle and AB and CD be the two parallel chords such that AB = 24 cm. Let length of CD be 2x cm. Drop OE and OF perpendicular on AB and CD from the centre O.

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.

Solution:

Concise Selina Solutions for Class 9 Maths Chapter 17Circles

Concise Selina Solutions for Class 9 Maths Chapter 17Circles

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.

Solution:

Let the radius of the circle be r cm.

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: (i) radius of the circle. (ii) length of chord CD.

Solution:

Concise Selina Solutions for Class 9 Maths Chapter 17Circles

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