9 class circle

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

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use
5 Geometry Page 6