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Byju's Answer
Standard XII
Mathematics
Condition for Coplanarity of Four Points
In a quadrila...
Question
In a quadrilateral,
A
B
C
D
is given that
∠
A
=
120
0
,
∠
B
=
∠
D
=
90
0
,
A
B
=
13
,
A
D
=
46
then
A
C
?
A
42
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B
62
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C
72
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D
44
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Solution
The correct option is
B
62
As given
∠
A
=
120
°
∠
B
=
90
°
∠
C
=
360
−
(
120
−
90
+
90
)
=
60
°
∠
D
=
90
°
We can see this is cyclic quadrilateral
A
C
=
2
r
(where
r
is radius)
A
C
=
B
D
/
sin
(
120
°
)
=
2
√
3
B
D
By the law of cosine of
Δ
A
B
D
B
D
×
B
D
=
13
×
13
+
16
×
46
−
2
×
13
×
46
cos
120
°
=
2883
A
C
=
2
√
3
√
2883
=
62
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0
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Q.
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A
B
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in which
A
D
=
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cm,
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