class 9 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(OA)= 10 cm
using pythagorous theorem

b) A 24 cm long chord is drawn in a circle having diameter 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

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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 =

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3a) in the given figure QR is the diameter of a circle with center O . If OP=13 cm and PR=
10 find the length of PQ
solution
Given :
To find :

statements Reasons

1) Being base angle of isosceles
tringle(OR=OP)

Being base angle of isosceles
tringle(OP=OQ)

3) sum of angles

4) using
pythagorous

676=100+

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 : base angles of isosceles triangle
To find :
statements base angles of isosceles triangle
1)
sum of angles of triangle
3)
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3) sum of angles of triangle

Or using

4)
pythagorous

5) Diameter =2 Radius

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= OP2+MP2
or

MP=12 perpendicular drawn from the centre
MP of circle to chord bisect the chord

12

Area of OM=5 cm and AB=8 cm . Find the area of
4b) in the given figure, O is the center

OP=5 perpendicular drawn from the centre
BD
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OP=5 perpendicular drawn from the centre
BD of circle to chord bisect the chord

=4

in right triangle OBD

Using Pythagoras theorem
OB2=

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 : radius ( r)=10,
To find : OP
construction: O&A are joined

i) AX= the perpendicular

ii) 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 square

using pythagorus theorem

Q6 same as example 5 and 6
7a) in the given figure ,O is the center of the circle. If AC=BD then prove that

Given :

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

Given : Reason s
to prove : Radii of
construction : Base angle of isosceles
supplement of equal angle
Statement
1. OC=OD From statement 3
2. given
3.
4 in
OC=OD
.
AC=BD

OA=OB(i.e. isosceles corresponding sides of
triangle)

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

=

Similarly RS=15

let OM=x then OR= 23-x
use Pythagoras theorem in

=

using Pythagoras theorem in

Radius of the same circle are equal

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now

=

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