CLASS 10 CIRCLE

Circle 1 to 24

Tuesday, December 8, 2020 9:28 AM

1) in the given figure find the degree meaurement of
solution : the relation between inscribe angle and opposite arc

or
being coplete turn

2 a) I sum of angle of trianlge
Ii)
or

Iii

3a ) solution

inscribe anlge is half of center angle standing on the same arce

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i) inscribe anlge is half of center angle standing on the same arce
236=reflex AOC
Ii)
acute AOC=124

3c)
solution

i)
ii)

Iii)

=220

Iv) inscribe angle is half of center angle
x=

4a solution inscribe anle on the same arc
I
Ii) geometry Page 2

=25
Iv)
4c) solution
i)

i) complete turn
Ii) reflex AOC =2
Iii)

Iv)

5b

i)
AOD +120=180

AOD=60

Ii)

6a ) solution Inscribe angle is half of centra angle standing on same arc
1
2,
3

=75

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7a being base angle of isosceles triangle
sum of anlges of traiangle OBC
Solution
1 anlge in semicircle
2.
angle on same arcAD
x=50
2.

50+y=9

7e
Solution
i)
ii)
iii)

7 f) exterior angle is equla to sum of two opposite interior anlge
solution
i) base angle of isosceles trianle
ii) exterior angle is equla to sum of two opposite interior anlge

=40
Iii)
Iv)

=40+20
=60

8a)

8a) exterior angle of cyclic quadrilateral is equal to opposite interior anlge

Solution geometry Page 4

i)

ii)
=
=110

9a solution
i)

10a)
Solution
i)
ii)

11) in the given figure alongside AB//CD prove that

given :
to prove :
construction: join A & D

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construction: join A & D

1 Alternate angle

2) AB//CD arcs of equal inscribe angle

12) in the given figure WZ//XY

Given : Reasons
To prove : Given
construction: arcs of equal inscribe angles

statement subtracting sides of

WZ//XY inscribe angle on equal angle s

being alternate angles

13) in the given figure ,

i)
Ii

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Given : Reasons
To prove : Given
inscribe angle on the same arc of a circle
statement inscribe angle on the same arc of a circle
from statement 1,2,3
AB//CD being alternate angle

14 ) in the figure AB and CD are two diameters of a circle with center at O if the
chord CE is parallel to AB and
Arc DEB

Given :
To prove :

statement Reasons

Base angle of isosceles triangle being OC= OB

corresponding angle

alternate angle

from statement 1,2,3,

Arce of equal center angle

B is the midpoint being
of

15 in the given figure two chord AB and CD intersect at right angle at X prove that

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Given : Reasons
To prove : Given
construction: join B& C
Relation between the inscribe anle and opposite
statement arce
Exterior angle is equal to sum of two opposite
90= angles
From statement 1,2,3

from statement
equating statements
16 ) in the given circle chords DE and FG intersects at X prove that

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Given :
To prove :
construction: join G and E

statement Reasons
Relation between the inscribe angle and opposite arc
relation between the inscribe angle and opposite arc
exterior angle and interior angle of triangle e
inscribe angle on equal angle s
being alternate angles

17) in the adjoining figure o is the center of a circle if then
proce that

Given :To prove :
construction: join G and E

statement Reasons
Base angle of a isosceles
relation between the inscribe angle and opposite arc
exterior angle and interior angle of triangle e
inscribe angle on equal angle s
being alternate angles

In the figure AP is a radius of the circle ABC and diameter of the circle APD .

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In the figure AP is a radius of the circle ABC and diameter of the circle APD .
Prove that AQ=QC.

Given :
To prove :
construction: join Q and P

statement Reasons
Angle on a semicircle
perpendicular drawn from the center of a circle to the chord bisect
the chord

19) In the given figure , two circles are intersecting at Mand N .PQ and RS pass
through M,R,P,S and Q are joined to N .Prove

Given : Reasons
To prove : Angle on same arc of a circle
construction:
vertically opposite angle
statement from statement 1 & 2
angle on same segment of a circle
from statement 3 & 4

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20) is an isosceles traingle and XY//BC. If XY cutes AB at X and AC at Y , prove
that four points X,B,C and Y.

Given : Reasons
To prove : Base angle of an isosceles triangle
construction: corresponding angle
from statement 1 & 2
statement Exterior angle is equal to opposite angle of quadrilateral

X, B ,C and Y are
concyclic

21) In the given figure ,ABC is a triangle in which AB=AC .Also a circle through
B and C intersects the sides AB and AC at the point D and E respectively . Prove that
AD=AE.

Given :
To prove :

construction:

statement Reasons
Base angle of an isosceles triangle
Exterior angle is equal to opposite angle of quadrilateral

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Exterior angle is equal to opposite angle of quadrilateral
from statement 1 & 2
Exterior angle is equal to opposite angle of quadrilateral
from the statement 3 and 4
being base angle are equal

22 In given figure , AD//BC and DP=DC , prove that

Given : Reasons
To prove : Base angle of an isosceles triangle
construction: Exterior angle of cyclic quadrilateral is equal to opposite
from statement 1 & 2
statement co-interior angle

from the statement 3 and 4

23) through each of the point of intersection of two circle , straight lines APC and BRD
are drawn . Prove that AB//CD.

Given :
To prove :

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construction: join P and R.

statement Reasons
Exterior angle is equal to opposite angle of quadrilateral
Exterior angle is equal to opposite angle of quadrilateral
being sum of angles of straight angle
from statement 1,2,&3
sum of interior angle

24) In the given figure , AB is diameter of a circle if
prove that

i)

ii)SFKB is acyclic quadrilateral

Given : Reasons
To prove : Given
construction: Angle on same segment of a circle
from statement 1 & 2
statement angle on a semi-circle

In common angle
from statement 3
remaining angle

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remaining angle
from statement 4

Sum of opposite angle is 180

24 b) in the given figure ,PQ is the diameter of the circle with center at If PX=XS prove
that OX//QS

Given :
To prove :

construction: Reasons

statement Common side
1) radii of a same circle
xo=ox Given
OS= by SSS axiom
SX= corresponding angle of a congruent triangle
base angle of isosceles triangle
XO//SQ Exterior angle of triangle of
being corresponding angle equal
Exercise

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