1. Find the length of the chord of a circle in each of the ...

Frank Solutions for Class 10 Maths Chapter 17

Circles

1. Find the length of the chord of a circle in each of the following when:

(i) Radius is 13 cm and the distance from the center is 12 cm

Solution:From the question it is given that,

Radius = 13 cm

Distance from the center is 12 cm

From the figure we can say that, PR = RQ

Because, perpendicular from center to a chord bisects the chord.

Consider the ¦¤PRO,

By using Pythagoras theorem, OP2 = OR2 + PR2

132 = 122 + PR2

PR2 = 132 ¨C 122

PR2 = 169 ¨C 144

PR2 = 25

PR = ¡Ì25

PR = 5 cm

Therefore, length of chord PQ = 2PR

= 2(5)

= 10 cm

(ii) Radius is 1.7 cm and the distance from the center is 1.5 cm.

Solution:From the question it is given that,

Radius = 1.7 cm

Distance from the center is 1.5 cm

Frank Solutions for Class 10 Maths Chapter 17

Circles

From the figure we can say that, PR = RQ

Because, perpendicular from center to a chord bisects the chord.

Consider the ¦¤PRO,

By using Pythagoras theorem, OP2 = OR2 + PR2

(1.7)2 = (1.5)2 + PR2

PR2 = (1.7)2 ¨C (1.5)2

PR2 = 2.89 ¨C 2.25

PR2 = 0.64

PR = ¡Ì0.64

PR = 0.8 cm

Therefore, length of chord PQ = 2PR

= 2(0.8)

= 1.6 cm

(iii) Radius is 6.5 cm and the distance from the center is 2.5 cm.

Solution:From the question it is given that,

Radius = 6.5 cm

Distance from the center is 2.5 cm

Frank Solutions for Class 10 Maths Chapter 17

Circles

From the figure we can say that, PR = RQ

Because, perpendicular from center to a chord bisects the chord.

Consider the ¦¤PRO,

By using Pythagoras theorem, OP2 = OR2 + PR2

(6.5)2 = (2.5)2 + PR2

PR2 = (6.5)2 ¨C (2.5)2

PR2 = 42.25 ¨C 6.25

PR2 = 36

PR = ¡Ì36

PR = 6 cm

Therefore, length of chord PQ = 2PR

= 2(6)

= 12 cm

2. Find the diameter of the circle if the length of a chord is 3.2cm and its distance from

the center is 1.2cm.

Solution:-

Frank Solutions for Class 10 Maths Chapter 17

Circles

From the question it is given that,

length of a chord is 3.2cm

Distance from the center is 1.2cm

Then,

From the figure we can say that, PR = RQ = 1.6 cm

Because, perpendicular from center to a chord bisects the chord.

Consider the ¦¤PRO,

By using Pythagoras theorem, OP2 = OR2 + PR2

OP2 = (1.6)2 + (1.2)2

OP2 = 2.56+1.44

OP2 = 4

OP = ¡Ì4

OP = 2 cm

Therefore, Diameter of the circle PS = 2OP

= 2(2)

= 4 cm

3. A chord of length 16.8cm is at a distance of 11.2cm from the center of a circle. Find

the length of the chord of the same circle which is at a distance of 8.4cm from the

center.

Solution:-

From the figure we can say that, PM = MQ = 8.4 cm

Because, perpendicular from center to a chord bisects the chord.

Consider the ¦¤PMO,

By using Pythagoras theorem, OP2 = PM2 + OM2

Frank Solutions for Class 10 Maths Chapter 17

Circles

OP2 = (8.4)2 + (11.2)2

OP2 = 70.56 + 125.44

OP2 = 196

OP = ¡Ì196

OP = 14 cm

Then, OP = OS = 14 cm because radii of same circle.

Now consider the ¦¤SLO

By using Pythagoras theorem, OS2 = SL2+ LO2

142 = (SL)2 + (8.4)2

SL2 = 142-8.42

SL2 = 196 - 70.56

SL2 = 125.44

SL = ¡Ì125.44

SL = 11.2 cm

Therefore, the length of chord SR = 2SL

= 2(11.2)

= 22.4 cm

4. A chord of length 6 cm is at a distance of 7.2 cm from the center of a circle. Another

chord of the same circle is of length 14.4 cm. Find its distance from the center.

Solution:-

From the figure we can say that, PM = MQ = 3 cm

Because, perpendicular from center to a chord bisects the chord.

Consider the ¦¤PMO,

By using Pythagoras theorem, OP2 = PM2 + OM2

OP2 = (3)2 + (7.2)2

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download