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Byju's Answer
Standard VIII
Mathematics
Construction of a Rhombus When One Diagonal and One Angle Are Given
In the rhombu...
Question
In the rhombus
A
B
C
D
, show that
4
A
B
2
=
A
C
2
+
B
D
2
.
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Solution
In
△
A
O
B
=
∠
O
=
90
∘
A
B
2
=
O
A
2
+
O
B
2
=
(
A
C
2
)
2
+
(
B
C
2
)
2
=
A
C
2
4
+
B
D
2
4
A
B
2
=
A
C
2
+
B
D
2
4
∴
4
A
B
2
=
A
C
2
+
B
D
2
.
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1
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If
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Q.
In the given figure, ABCD is a rhombus. Then,
(a) AC
2
+ BD
2
= AB
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(b) AC
2
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2
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(c) AC
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(d) 2(AC
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