Ex 7 circle 8:23 PM

Thursday, December 3, 2020

1a) A 16 cm long chord is drawn in a circle l having radius 10 cm .What is the distance of the

chord from the Centre?

Solution

Length of chord AB= 16

AC= perpendicular drawn from the centre

of circle to chord bisect the chord

Radius(OC)= 10 cm

using pythagorous theorem

b) A 24 cm long chord is drawn in a circle having diameter r 26 cm . What is the distance of the

chord from the center of the circle?

Length of chord PQ= perpendicular drawn from the centre

AC= of circle to chord bisect the chord

Radius(OR)= [ diameter = 2 radius]

using pythagorous theorem

c) Find the length of a chord , which is at a distance of 6 cm from the center of circle of radius

10 cm

solution

OC=

Radius(OC)= 10 cm

using pythagorous theorem

AC= perpendicular drawn from the centre

of circle to chord bisect the chord

5 Geometry Page 1

d) the radius of a circle is 13 cm and the length of chord is 24cm find the distance of the chord

form the center

Length of chord AB= 24

AC= perpendicular drawn from the centre

of circle to chord bisect the chord

Radius(OC)= 13 cm

using pythagorous theorem

2a) in the given figure , o is the center of a circle > if

Solution: perpendicular drawn from the centre

Length of chord MN= of circle to chord bisect the chord

AM=

OM=3

using pythagorous theorem

diameter =

b) In the given figure O is the center of a circle . if Find

the length of diameter

solution

Length of chord AB= 16

AM= perpendicular drawn from the centre

of circle to chord bisect the chord

OM=8

using pythagorous theorem

diameter =

5 Geometry Page 2

3a) in the given figure QR is the diameter of a circle with cente O . If OP=13 cm and PR=

10 find the length of PQ

solution

Given :

To find :

statements Reasons

1)

3)

4)

using pythagorous

b) in the given figure ,MN is the diameter of a circle with center O .If QM =24 c m and QN=

32 cm find the length of OQ

solution Reasons

Given :

To find :

statements

1)

3)

Or 2x+2y=

x+y=

4)

using pythagorous

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4) a) In the figure along side O is the center of the circle of radius 13 cm .A chord MN is at a

distance of 5 cm from the center . Find the area of the

Solution

OM=13

OP=5

in right triangle OPM

Using Pythagoras theorem

OM2=

MP perpendicular drawn from the centre

of circle to chord bisect the chord

Area of OM=5 cm and AB=8 cm . Find the area of

4b) in the given figure, O is the centre

OP=5

in right triangle OBD

Using Pythagoras theorem

OB2=

BD perpendicular drawn from the centre

of circle to chord bisect the chord

Area of

5a) In the adjoining circle radius is 10 cm if chord AB= chord CD=16 cm

and What is the meaure of OP?

solution

Given :

To prove :

construction

AX= the

5 Geometry Page 4

To prove :

construction

AX= the

in right angle triangle AOX

OX=OY equal chord are equidistance from the

OXPY is a square

OX=XD= 6 being the sides of the

using pythagorus theorem

Q6 same as example 5 and 6

7a) in the given figure ,O is the cente of the circle. If AC=BD then proce that

Given : Reason s

to prove : supplement of equal angle

construction : given

Statement

1. OC=OD

2.

3.

4 in

OC=

.

corresponding sides of

Q 8 is similar to example 9

9) in the given figure PQ and RS are two chords of a circle with center O where PQ =16 cm RS=

30 cm and PQ//RS . If the lie MON of length 23 cm is perpendicular to both PA an RS , fin the

radius of the circle .

solution

Join OP and OR

let OM=x then OR= 23-x

use Pythagoras theorem in

use

5 Geometry Page 5

use

5 Geometry Page 6