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Byju's Answer
Standard VI
Mathematics
Quadrilaterals
Construct a c...
Question
Construct a cyclic quadrilateral
A
B
C
D
such that
A
B
=
3.4
c
m
,
B
C
=
4.2
c
m
,
A
D
=
2.7
c
m
and
∠
A
B
C
=
60
∘
.
Then, sum of the lengths of the diagonals is:
A
8.3
c
m
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B
9.2
c
m
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C
10.6
c
m
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D
7.1
c
m
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Solution
The correct option is
A
8.3
c
m
Draw a line segment
B
C
of length
4.2
c
m
.
Draw a line at an angle of
60
o
by taking
B
C
as base and
B
as vertex.
Cut an arc of
3.4
c
m
from
B
. This arc cuts the line at point
A
.
Join
A
B
.
Draw perpendicular bisectors of
A
B
and
B
C
. These perpendicular bisectors cuts each other at point
O
.
Draw a circle of radius
O
B
and center
O
, this circle touches
A
,
B
,
C
.
Mark an arc of length
2.7
c
m
on circle from point
A
. This arc cuts the circle at point
D
.
Join
A
B
C
D
.
A
B
C
D
is the required cyclic quadrilateral.
l
(
A
C
)
=
3.8
c
m
(measurement)
l
(
B
D
)
=
4.5
c
m
(measurement)
A
C
+
B
D
=
8.3
c
m
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Similar questions
Q.
Construct a cyclic quadrilateral
A
B
C
D
such that
A
B
=
3.4
c
m
,
B
C
=
4.2
c
m
,
A
D
=
2.7
c
m
and
∠
A
B
C
=
60
∘
.
Then,
l
(
C
D
)
=
?
Q.
Construct a cyclic quadrilateral
A
B
C
D
such that
A
B
=
3.4
c
m
,
B
C
=
4.2
c
m
,
A
D
=
2.7
c
m
and
∠
A
B
C
=
60
∘
.
Then,
m
∠
A
D
C
(in degrees)
=
?
Q.
Construct a cyclic quadrilateral
A
B
C
D
such that
A
B
=
3.4
c
m
,
B
C
=
4.2
c
m
,
A
D
=
2.7
c
m
and
∠
A
B
C
=
60
∘
.
Then, diameter of the circle circumscribing the cyclic quadrilateral is:
Q.
Construct a cyclic quadrilateral
A
B
C
D
such that
A
B
=
6
c
m
,
∠
A
=
60
∘
,
∠
A
B
D
=
30
∘
and
∠
C
B
D
=
20
∘
.
Then, sum of the length of the diagonals is:
Q.
Construct a cyclic quadrilateral
A
B
C
D
with
A
B
=
5
c
m
,
B
C
=
4.3
c
m
,
∠
A
B
C
=
60
∘
and diagonal
B
D
=
5.6
c
m
.
The length of the diagonal
A
C
(in
c
m
) is :
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